You'll have to enter the kitty twister club first and find someone to talk to who's interested in your highscore. You won't have to play rabbit run again after talking to that guy, once you have the highscore, you're good.
The tickets for the bar are sold out, but the bouncer will tell you who bought the last ticket - look for the proud owner of the last ticket up in the mountains near the coast, maybe he's willing to give it to you.