In English, it is not OK to use 'me + _________ing.' Example 'me eating, me sleeping, me disturbing.' Those are wrong phrases. These are correct, 'My eating, my sleeping, my disturbing." (I hope my eating doesn't make you hungry). You wouldn't say, 'Excuse me disturbing you.' That's wrong. You can say, "Excuse me. I hope I am not bothering you." or "I hope I am not disturbing you," Many time you can say, 'Excuse me'. Or, after you talked to someone and they couldn't help you, you can say, "Please excuse my bothering you,"

Very simple: Sorry to bother you.

They are quite similar. 'Bothering' could mean a longer interruption, such as asking a question. 'Disturbing' could be something as little as bumping into someone. But generally, they can be used interchangeably. But - in most cases, just 'excuse me' is fine, 'bother/disturb is understood/implicit.