To prevent hash reuse you can hash the password with a constant per site salt, e.g. bcrypt(sha256("news.ycombinator.com",password))
If an attacker is able to obtain password hashes from two different sources, one of which is storing passwords with bcrypt(sha256($password)) and the other of which is storing them as plain sha256($password), and attacker can use uncracked SHA-256 hashes from the second site as candidate passwords to try and crack the hashes from the first (more secure) site. If passwords are re-used between the two sites, this can effectively allow the attacker to strip off the Bcrypt layer, and to crack the much easier SHA-256 passwords.
OPs solution is neither a salt, nor a pepper. It is however, a nice way to prevent the above problem.