For me to enter into a relationship someone, we’d have to go through some kind of dating phase first. That’s the time when, through conversations, shared activities, over dinner, on car drives, etc., people talk, and usually at least some of it is about their past. That’s how people get to know each other, and learn if they’re compatible enough to continue dating, or enter into something more.
Without this introduction, I don’t think I’d enter into a relationship with someone. It’s not a judgment, it’s more like a vital step, sort of like how you can’t get to the second floor without stairs or an escalator. It’s part of the flow.
Explaining an embarrassing past might be rough, but it’s not like you have to drop it all on the first date, or even the fifth. That’s why people sometimes date for years before getting married. Perhaps it will help if you don’t feel forced to explain everything right away. Just let it come out naturally, at the right time for any given factoid or anecdote. If they’re the right kind of person for you, you won’t be able to scare them away – especially as they get to know you, gradually and at a natural pace.