We generally use wood glue as it wont adhere to the metal screw. Matchsticks are made for this type of thing. Matchsticks and glue and you can put the screw straight back without waiting for it to dry. Just screw it in, when the glue dries in an hour or so, you can then tighten it up a bit more.
There was no need to tin the ground wire either, as long as it is in contact with the bridge, jobs a groovy one.