What kind of locks do I get for a jack and jill bathroom so that you can have privacy in the bathroom as well as in both bedrooms?
You already answered it in your question. You need to look for privacy door locks. Also be aware that there are privacy locks that allow you to unlock from both sides (think standard bedroom lockset that gives you a small hole or allows you to use a coin to unlock from outside). If you just have family members any standard privacy lock is fine. If you have strangers you need to make sure the model doesn't allow the option of unlocking from other side.
You need a lock that can be locked from either side, if you want bedroom and bathroom privacy. The person using the room would naturally be able to exit via their own entrance, but not the other, and would be able to lock others out from both sides, while using the room. No keys should be necessary. Everyone simply needs to remember to unlock the other door from the inside before leaving.