How to stabilize a bike?

First what kind of bike you are creating? Physics or just model with animations? Be more precise of what you are doing , what you want get and what are problems. It is quite hard to guess without that information.

also you can always google to get some results like:
https://forums.unrealengine.com/community/work-in-progress/115275-wip-wheelz2-physics-bike-game

Ask that guy maybe he is willing to share how he did them.