All kidding aside, I just come out with the truth when I approach women like that and in that circumstance. We all know it's not the proper place to approach women, so keep it brief, and I'd (personally) tell her something very brief with "I don't want to let this opportunity to slip by", because that is in fact the truth.
If I see an irresistable woman, I tell her that. If you are sincere (and she's gotta feel you too), then she'll bite. She's fucking human. Life isn't as smooth as we'd like it sometimes. Go for it. Like you said, if she says no, just keep woking out. Hopefully you'll be both telling this story to your kids one day. If so, I expect karma.