I think pointing out the pet adoption behavior is a really good idea. It is something not shared by the population at large. What a cute symptom, frankly! Post a picture of the kitten!

I also really like Anika's comparison with diabetes which you do not necessarily see. Of course, your mother would counter that there is a blood test for diabetes and no blood test for bipolar. Be prepared for that. You may want to mention that although there is no blood test for bipolar, many bipolar treatments involve regular bloodwork to determine the levels of drugs in the body. So there is something concrete to hold on to for her.

Do you spend when manic? Do you buy obsessively, a lot of the same or similar goods? This would be evidence to show that you are bipolar. This is very concrete (and quite draining on bank accounts).

Above the regular posts here is a thread on recommended books for bipolar - you may want to read some and then select one to give to her to read, when you are ready.