Interesting question. Let’s break it down:

Can Velociraptor sit?

Yes, probably. Fossil evidence shows us that small theropods like Velociraptor could crouch down in a bird-like manner, including footprints left in a sitting position and skeletons preserved in place sitting over their nests.

They might not be able to sit exactly like us. They might need a modified seat for the shape of their dino-butts and tails.

Could Velociraptor pedal?

This is hard to know. I don’t know of biomechanical studies to indicate the full range of motion they had in their legs. But in the absence of that information, we can look to their living relatives, and it looks like modern birds can pedal. So there’s a good chance Velociraptor had a similar capability.

Could Velociraptor hold the handlebars?

Not traditional horizontal handlebars. Movies love to show dinosaurs with the classic “palms-facing-down” hand-pose, but they actually were unable to do that. The hands of Velociraptor were more-or-less stuck in a “palms-facing-inward” position. And they wouldn’t necessarily be able to grip quite like we do.

But you could probably make some sort of specially-shaped handlebars for their hands to grasp / sit upon.

Could Velociraptor balance on a bike?

This one is hard to answer. Living dinosaurs (birds) obviously have a great sense of balance, given their ability to fly, land, and perch stably. Perhaps Velociraptor did as well.

It has been suggested that the claws of small “raptors” may have been used in part for climbing or even for pinning prey to the ground, both of which, if true, would benefit from good balance.

Actually, the “pinning prey” hypothesis involves these dinosaurs spreading out their wings to balance themselves, so maybe Velociraptor would spread its wings out to the sides for balance.

But then it isn’t using handlebars, so how would it turn? Perhaps a “rear handlebar” could be designed so they could use their tails to turn the bike instead of their hands.

Conclusion

Yeah, maybe!

I think a bicycle could be built specifically for the body-plan of Velociraptor. It would need to be a highly-modified bike, and a small one (considering Velociraptor was under 3 feet tall). Whether or not it would be any good at riding, or would have any interest in doing so, will obviously require more paleontological research.

So somebody draw up a blueprint for this dino-bike!