Disclaimer: I am not a lawyer, so to be on the safe side, you might want to contact one. All information is supplied without guarantee.
There is a wikipedia article about Software relicensing which you probably should check out.
Also on the opensource guide on the legal guide section 6 "What if I want to change the license of my project?" you can see that actually changing a license is not always that trivial.
If a library version comes with an opensource license, I personally would expect, that only on a version update it might change.
So I would expect you do not have to strip out all the code related to it, if you do not update the library in that case.
Btw. you should check not only the Bullet Physics license, but also the licenses of the used libraries inside of Bullet Physics.
Unity and Unreal may be free to use in the beginning, but you will have to pay for using them if your game is not for free and you earn enough money with it.