Do you know about the PHP function password_hash(), it is the recommended way to hash passwords. It automatically generates a cryptographically safe salt for each password and includes it in the resulting 60-character string.
$2y$10$nOUIs5kJ7naTuTFkBy1veuK0kSxUFXfuaOKdOKf9xYT0KKIGSJwFa
The example above is a possible result of password_hash(), have a look at the part $nOUIs5kJ7naTuTFkBy1veu
, this is the generated salt and it will be used by the function password_verify() to check the password.
You won't have to worry about the salt anymore, no additional database field is necessary, just store the hash and you are fine!
The easiest way to migrate your passwords, is to wait for the user to login the next time. When he enters the password, you can check if the hash is already migrated, then check with password_verify(). If it is not yet migrated then check it with your old vBulletin code, if the password is correct then use password_hash() to generate a new hash and store it.