We just installed a new faucet in our bath tub. The first handful of water that comes out each time is rusty looking, then clears up. Is this a problem and how do we fix it?

It should clear up shortly. When replacing the faucet you disturbed the rusty threads of the pipes. Since you say it is rust you must have galvanized plumbing pipes. If you don't have galvanized pipes then I don't know where the rust is from.