I'm not sure an attorney is the right person to ask. So, since I'm not an attorney, I'll give you a not-an-attorney answer. Right now it's not going to be a big deal at all. You'll have to explain it, show that you're contrite, your attitude has changed, etc etc. Own it and all of that. With that said, they are positively desperate to hire people, so if you don't walk in and tell them that you're glad you hit that church bus and you'd do it again given a chance, you're going to be fine.
Even if you "only have one" by the time you start interviewing, it would probably be best to disclose both if the application form asks for accidents or driving infractions, or if asked about it in the interview. Even if an accident or infraction is expunged there may still be a record of it that could come up in the background check. As Boris pointed out, in today's hiring climate, regionals are willing to accept a lot of major black marks, but if it appears you were dishonest on the application or interview that is generally grounds for termination.