I agree with Traveling Lady. If you care about someone, then show it by not getting into the drunk-hookup scenario. It confuses things a lot for everyone involved.
Move on from the night of regret. You apologized already. She accepted the apology right? So let it go.
If this is someone you felt a spark with, well, be her friend. Sure, reach out, see where she is now. But do it with no expectations. She may not be capable of being friends with a guy, but if it means this much to you, you owe it yourself to check it out. If, in time, something more develops, you will know it is because you laid the groundwork of friendship, which is necessary in any relationship.
Best to you