Can one night stands turn into a stable relationship?

so i met this guy and i was really drunk and we ended up hooking up. the next day i immediately regreted it because 1) i dont do that sort of thing and 2) i really like him and dont want him to think i was just a call. That same night (after these events had taken place) he still asked for my number and asked if he could take me out to a proper dinner, but im just afraid hes going to reconsider or not take me seriously. is there anyway things could work, or did i totally screw it up? Guys who are responding to this question... what would you do in his situation? Thanks.