It implies that the person speaking is hesitant to ask, perhaps because they are unsure of the response or worried about appearing intrusive.
Here are some ways to rephrase "may to ask" using "ventured":
* "I ventured to ask..."
* "I dared to ask..."
* "I hesitantly asked..."
* "I took the chance to ask..."
For example:
* Original: "May I ask what you're working on?"
* Using ventured: "I ventured to ask what you're working on?"
"Ventured" adds a sense of caution and uncertainty to the question, indicating that the speaker is approaching the topic with some trepidation.