There's already a parallax effect based on distance, I don't experience any nausea, so I'd have no idea how to fix it either.The bike Minigame is nauseating, it's not unenjoyable, it's just that the background makes me feel as if I'm spinning, I'm not sure how to fix it, maybe add some parallax effect to the city background, so the effect is less noticeable?
Unless..you mean't the minigame to induce nausea?
I'm going to assume that only happens with high speeds? Let's say 1000+? In that case you can simply crash your bike on purpose once you reach that score, and start over if needed.
There's no "win condition", you can play that as little or as much as you want/can, and you'll be rewarded anyway. It's designed to be played on any skill level. You can also skip it entirely by using FPs.