Sounds like a scene from “Breathless”. It’s been a long time since I’ve seen it.
I’m pretty sure it was earlier in the film. Somewhere in the first third, IIRC. It might be the first time Sheen and the female lead meet, or shortly thereafter.
OK, update: It’s not Yes Man or If, and I think I’ve found the scene in Hot Shots people are talking about - when Sheen first meets his love interest, they have a contest of sorts with him on his motorcycle and her on horseback, as she does various tricks and he attempts to mimic them. I’ve been through just about the whole movie and that’s the only thing I could find, but several people seemed to remember a scene more like the one I’m looking for, and Hot Shots “feels” like the right kind of movie… hrm.
I haven’t been able to check out the suggestions of Grease 2 and Officer and a Gentleman yet, but Grease 2 seems to have gotten the greatest vote of confidence on here so far, so I have a feeling it will end up being that. I’ll keep looking though - you guys are very helpful 
Wasn’t there a scene like that in Revenge, with Kevin Costner and Madeline Stowe?
Also in the 1994 Charlie Sheen movie The Chase, although he and the girl weren’t handcuffed when they got bizzay in the driver’s seat of a car under police pursuit.
[Sorry, disregard this]
I found the Revenge scene - very similar, but it’s on a Jeep, and I’m positive it was a motorcycle.
At the end of Reckless, (a very young and hot) Daryl Hannah rides off on (very young and hot) Aidan Quinn’s motorcycle with him. In Purple Rain, Prince drives Apollonia around on his tiny purple riceburner. I wonder if there was a scene with James and Laura on James’s bike in Fire Walk With Me?
I’m gonna echo the Grease 2 vote. Michelle Pfeiffer straddling the front of Max Caulfield’s bike (sans helmet) is definitely part of their romantic sunset ride.
It was, in fact, Grease 2! Borrowed a friend’s copy today. Thanks for the help everyone, there’s no way I would’ve remembered it in a million years. You guys are awesome. There’s one other movie scene I’ve been trying to identify forever, maybe I can finally get that cleared up too. I’ll make a new thread, maybe after helping out some other folks looking for similar help.