How many times can you bleach your hair until its overly processed?

In a lifetime, several times. In a short period of time, it's not recommended more than once.

You will know if your hair is over processed by its unhealthy (and often unflattering) appearance. It may appear dry, frizzy, brittle, excessive split ends, dry and/or itchy and/or red scalp, easily breaking during even gentle brushing, or a combination of the above.

BUT if you take Excellent care of your hair, deep condition once a week or more and stuff like that, I would say around 10 times if you have strong hair.. I have bleached mine about 11 times and it still looks healthy. BUT I didn't go crazy and bleach it white every time or anything, it gradually went white (I use semi-perm hair dyes so that is good).