According to Webster's 1828 dictionary, this is the definition of a heretic:

-A person under any religion, but particularly the christian, who holds and teaches opinions repugnant to the established faith, or that which is made the standard of orthodoxy. In strictness, among christians, a person who holds and avows religious opinions contrary to the doctrines of Scripture, the only rule of faith and practice.

So according to the definition, I would say that person would be a heretic if he started teaching false doctrine. In many cases though someone who has a false Bible, has it under ignorance. I would not consider them a heretic unless they practiced and preached unbiblical doctrine.