A word similar to "shame" that has a positive connotation

Thesaurus work gives many possibilities but none seems to fit the subtle change of meaning that you seek. The nearest I can get from other related concepts is “presumptuous”, which admits your negative embarrassment in asking, but keeps the balance of positive respect between you and the other person.

Shame is negative, so a word with a positive connotation would be a very different word.

You mention modesty in your question, but that isn't in the sentence you wrote. Discretion, or being discreet, is sometimes a positive reason to hide something.

A positive word for shame about asking for a favor

diffident adjective

diffident adjective

dif·​fi·​dent | ˈdi-fə-dənt , -ˌdent

Definition of diffident

1 : hesitant in acting or speaking through lack of self-confidence

2 : RESERVED, UNASSERTIVE

https://merriam-webster.com/definitions/diffident

The closest words that I found are "considerate" and "thoughtful"

For example, consider the following sentences.

He was very considerate about asking for a favor because he was already indebted to her.

He was very thoughtful about asking for a favor because he was already indebted to her.

These words are not exactly what I was looking for because of the following reasons.

• Both of these words are an action and not a feeling.
• "Considerate" is mostly used for the person who is on a higher ground.

However, these words somewhat serve the purpose.

Interesting Fact:

There is a word for this in Urdu language called "Haya"

• "Haya", noun translates to "Modesty"
• "Haya Aana", verb translates to the positive shame that I was talking about. The person is already indebted and feels shame in inconveniencing the other person by asking for another favor.

How about abashed? Not as assertive as ashamed and invokes the more complex feeling you describe. " made to feel uncomfortable, disconcerted, or embarrassed by something that has happened or been done or said" https://www.merriam-webster.com/dictionary/abashed