No, each site is essentially isolated from the other sites, as far as reputation is concerned. You cannot transfer bounties from reputation earned elsewhere.
The only exception is the association bonus which is given to you because you've learned the basics of the Stack Exchange model.
If you could transfer reputation, then anyone with an account on a busy site such as Stack Overflow could monopolize attention on a smaller site. I could use my 200k on Stack Overflow to buy a lot of eyeballs over on, say, Pets.stackexchange.com. That would not be fair to the other regular Pets supporters without a big fat SO account to draw from.