Asking for a recommendation letter (Post-Doc) when you have Bipolar Disorder
Depending on the level of trust you have, you might consider revealing some of your medical history along with assurance that the issues are under control and won't result in future problems. But you also need to let them know whether it is ok or not for them to pass on details in letters. This is probably not advised. A LoR saying you had previous medical issues, now resolved, that affected performance is about as far as anyone should go. But make sure you set the limits. 

However, also consider whether your recent performance, especially with letter writers, is good enough that they will discount/ignore the earlier problems altogether, and only write about your current performance and your likelihood of success. 

And, even if you decide to tell some people, it might be best to limit the details. The important message is really only "medical condition", "now resolved". Beyond that may be more personal than you are comfortable with. 

You might even consider asking them, provided your relationship is strong enough, whether your past performance would color their recommendation. If they hesitate to say no, then it might be more useful to give them the key message - medical, resolved.