I want to get a Crobat. My Zubat is at 21. If it evolves into a Golbat will it loose all of its happiness and go back to the base happiness?
No, it would not. Evolution does not effect happiness in any way. So you can evolve Zubat without worrying about its happiness resetting.
It will not reset the happiness, infact the happiness will increase (as you have gained a level).