In Jaami‘ Al-‘Uloom wal-Hikam, Ibn Rajab  said, "Know that there are two types of bashfulness: that which is innate and not acquired. It is one of the most sublime morals that Allah The Almighty grants to the slave. Therefore, it was narrated that the Messenger of Allah  said: "Bashfulness brings only what is good." It prevents one from committing evil deeds or adopting bad morals. On the other hand, it urges adopting noble and sublime morals. Given this, bashfulness is one of the characteristics of faith."

It was narrated on the authority of ‘Umar, may Allah be pleased with him, that he said, "A person who is bashful does not disobey Allah The Almighty, and a person who is pious will be saved."

Al-Jarraah ibn ‘Abdullaah Al-Hakami  the warrior of the people of Ash-Shaam, said, "I abandoned sins for forty years out of bashfulness and then I achieved piety."  Then he added, "It was narrated in a Mursal Hadeeth by Al-Hasan, may Allah be pleased with him, that the Prophet  said: "Bashfulness has two forms: a type that is part of faith and a type that is impotence." This could be the words of Al-Hasan, may Allah be pleased with him.

Bishr ibn Ka‘b Al-‘Adawi  said to ‘Imraan ibn Husayn, may Allah be pleased with him, "We find in some books that a form of bashfulness is due to showing tranquility and veneration towards Allah The Almighty and a form of it is due to weakness." ‘Imraan, may Allah be pleased with him, became angry and said, "I narrate to you from the Messenger of Allah  and you object it!"

It is as ‘Imraan, may Allah be pleased with him, said, the praiseworthy bashfulness meant in the words of the Prophet, , is that moral which urges doing what is good and abandoning what is evil. As for weakness and impotence which entail neglecting the rights of Allah The Almighty or His slaves, this is not a part of bashfulness. Rather, it is weakness, debility, impotence and meanness.

Bashfulness of Moosa, may Allah exalt his mention:

It was narrated on the authority of Abu Hurayrah, may Allah be pleased with him, that the Messenger of Allah, , said: "Moosa was bashful and used to cover his body completely out of his bashfulness." [Al-Bukhari]

It was narrated on the authority of Abu Sa‘eed Al-Khudri, may Allah be pleased with him, that he said, "The Prophet  was more bashful than a virgin in her private room. If he saw a thing which he disliked, we would recognize that (feeling) in his face." [Al-Bukhari]

As for his bashfulness of his Lord, it was narrated on the authority of Maalik ibn Sa‘sa‘ah, may Allah be pleased with him, that when prayer was obligated as fifty prayers per day, the Prophet , kept going and coming between Moosa, may Allah exalt his mention, and his Lord asking Him to reduce them until they finally became five. Moosa, may Allah exalt his mention further advised him to return to his Lord and ask Him to reduce the prayers, but the Prophet, , responded: "I kept asking my Lord until I became bashful. Rather, I will be satisfied and submit." [Al-Bukhari]

It was narrated on the authority of ‘Aa’ishah, may Allah be pleased with her, that she said, “A woman asked the Prophet  how to wash herself after menstruation. She mentioned that he taught her how to take a bath and then told her to take a piece of cotton with musk and purify herself. She said, "How should I purify myself with that?" He (the Prophet ) said "Purify yourself with it, Subhaan-Allah (Glory be to Allah)!" and he covered his face with his hand." ‘Aa’ishah, may Allah be pleased with her, added, "I pulled her towards me for I understood what the Prophet  meant and, therefore, said, 'Follow (with the cotton) the trace of the blood.'"[Muslim

Bashfulness of Abu Bakr, may Allah be pleased with him:

Once, As-Siddeeq, may Allah be pleased with him, addressed the Muslims and said, "O people! Show Allah His due reverence. Since I have given the Messenger of Allah  the pledge of allegiance, by Allah, I never went out to answer the call of nature without having my head covered out of bashfulness of Allah The Almighty." [Makaarim Al-Akhlaaq]

He also said, "A person who lacks bashfulness lacks piety; and if a person lacks piety, his heart dies."

He also said, "A person who is bashful does not disobey (Allah The Almighty); a person who does not disobey is pious; and a person who is pious will be saved." 

Bashfulness of ‘Uthmaan, may Allah be pleased with him:

Talking about ‘Uthmaan, may Allah be pleased with him, and his bashfulness, Al-Hasan Al-Basri  said, "He used to be alone at home with the door closed, and when he took off his clothes to wash himself, his bashfulness prevented him from standing up straight."

Bashfulness of Abu Moosa Al-Ash‘ari, may Allah be pleased with him:

It was narrated that he said: "I perform Ghusl (ritual bath) in the house while the lights are out, nevertheless, I cannot stand upright unless I put on my garment due to my bashfulness of my Lord." [Az-Zuhd by Imaam Ahmad]

It was narrated on the authority of Qataadah, may Allah be pleased with him, that he said, "Abu Moosa used to perform Ghusl in the house while the lights were out while crouching and bending his back. He did not stand upright until he put on his clothes."

It was narrated on the authority of Anas, may Allah be pleased with him, that he said, "Abu Moosa Al-Ash‘ari, may Allah be pleased with him, used to wear his clothes when he went to sleep out of fear that his ‘Awrah (private parts) would be exposed."

Bashfulness of Abu Muslim Al-Khawalaani :

Abu Muslim Al-Khawalaani, may Allah have mercy on him, said, "It is from the favors of Allah The Almighty upon me that I have not done anything to make me bashful for thirty years except for having sexual intercourse with my wife."

A person who is bashful of people seeing him commit an evil act, should be more bashful of Allah The Almighty. Consequently, he should neither neglect an obligation nor commit a sin as he knows that Allah The Almighty sees him and that He will inevitably call him to reckoning on the Day of Resurrection. Therefore, he feels bashfulness of his Lord. 

It was narrated on the authority of Ibn Mas‘ood may Allah be pleased with him, that the Messenger of Allah, , once said to his Companions, may Allah be pleased with them: "Show due reverence to Allah." They (the Companions, may Allah be pleased with them) said, "We show (Allah The Almighty) due reverence, O Messenger of Allah."He said: "It is not that (which you think). Rather, a person who shows Allah due reverence should preserve his head (i.e., by not using it to commit any act of disobedience) as well as what it includes (i.e., the eyes, ears and mouth) and preserve his belly (i.e., from eating unlawful food) and what it includes and should constantly remember death and perishing. Whoever pursues (the reward of) the Hereafter should abandon the pleasures of this worldly life. Whoever does so has shown due reverence to Allah." [Ahmad] 

“His head as well as what it includes” means that the head and its external and internal senses should be used only in permissible things. 

It was narrated on the authority of Mu‘aawiyah ibn Haydah, may Allah be pleased with him, that he said, I said, "O Messenger of Allah  from whom should we conceal our ‘Awrah (private parts) and to whom can we expose it?" He replied: "Conceal your ‘Awrah except from your wife and from whom your right hands possess (slave-girls)." I then asked, "O Messenger of Allah, (what should we do) if the people are assembled together?" He replied: "If you can do so in a way that no one looks at it (‘Awrah), then no one should look at it." I then asked, "O Messenger of Allah, if one of us is alone, (what should he do)?" He replied: "Allah is more entitled than people that bashfulness should be shown to Him." [Ahmad]

Bilaal ibn Sa‘d  said, "Do not look at the smallness of the sin, but look at the greatness of the one you are sinning against."

Once, when a man was alone with a woman and he wanted to have unlawful sexual intercourse with her, she said to him, "Look if there is anyone who can see us?" He replied, "Only the stars see us." She asked, "Then where is The One who created them?

In Madaarij As-Saalikeen, Ibn Al-Qayyim  divided bashfulness into ten parts: bashfulness out of committing wrongdoings, bashfulness out of being negligent, bashfulness out of exaltation, bashfulness out of generosity, bashfulness out of chastity, bashfulness out of belittling and disdaining oneself, bashfulness out of love, bashfulness out of worship, bashfulness out of honor and glory, and bashfulness of the person who is bashful of his own self.

Ibn Al-Qayyim  elaborated on this and here I will mention them briefly: 

1- Bashfulness out of committing wrongdoings:

An example for this, Aadam (Adam), may Allah exalt his mention, tried to flee in Paradise. Thereupon, Allah The Almighty said to him: "Are you fleeing from Me, O Aadam?" He replied: "No, my Lord. I am fleeing out of bashfulness of You."

Another example is bashfulness of the prophets, may Allah exalt their mention, on the Day of Resurrection although they have no faults to discredit their high and sublime ranks.

2- Bashfulness out of being inelegant:

An example of this is bashfulness of the angels, may Allah exalt their mention, who exalt Allah The Almighty night and day and do not slacken. On the Day of Resurrection, however, they will say (to Allah), "Glory be to You. We did not worship You as You are due." ---

3- Bashfulness out of exaltation:

This aspect of bashfulness occurs due to knowledge. The degree of one’s bashfulness is according to the degree of his knowledgeable of his Lord. For example, it was narrated that ‘Amr ibn Al-‘Aas, may Allah be pleased with him, used to say, "By Allah, I was the most bashful of people with the Messenger of Allah . I never gazed at the Messenger of Allah  nor argued with him on a matter I desired until he died, as I was bashful of him." [Ahmad]

 4- Bashfulness out of generosity:

The Prophet, , was bashful of the guests whom he invited to the wedding banquet of Zaynab, may Allah be pleased with her. They ate and then sat for a long time. The Prophet, , was bashful to tell them to leave. Thereupon, Allah The Exalted revealed the verse in which He Says (what means): {…without seeking to remain for conversation.} [Quran 33:53]

5- Bashfulness out of chastity:

For example, ’Ali ibn Abi Taalib, may Allah be pleased with him, was too bashful to ask the Messenger of Allah, , about pre-ejaculatory fluid as he was his son-in-law. It was narrated on his authority that he said, "I used to discharge pre-ejaculatory fluid frequently. I told Al-Miqdaad ibn ’Amr to ask the Prophet  and he did. The Prophet  replied: "You should perform ablution."

The wording of another narration reads: "I used to discharge pre-ejaculatory fluid frequently. Being the son-in-law of the Prophet  I told a man to ask him about it. So the man asked the Prophet  about it and the Prophet  replied, "Perform ablution after washing your organ (penis)." [Al-Bukhari]

6- Bashfulness out of belittling and disdaining oneself:

An example of this is the bashfulness of the slave of Allah The Almighty in front of his Lord when he asks Him for his needs out of belittling and disdaining himself. It is mentioned in an Israelite reported citation that Moosa (Moses), may Allah exalt his mention, said: "O Lord, I find myself in need of something in this world but I feel bashful to ask you." Allah The Almighty Says: "Ask Me…..even (if it were for) salt for your dough and the fodder for your sheep."