The buzzing comes from different places so its a process of elimination really.
1/ The main culprit is the saddle grub screws coming loose, so they fall short and rattle against the bridge assey : use grease, vaseline or similar to lubricate the threads on each screw.
2/ The saddles can rattle against each other although string tension should hold them tight in place. If you drop tune you may need to compensate by : putting something between each saddle to stop them rattling again.. vaseline, etc.
3/ If the rocking bridge is'nt fully pushed one way or the other the posts can rattle in the post holes. This is rare but : tape would cure that. If you use the trem just one piece of tape will do, dont secure the bridge.
4/ Sometimes the bridge post screws also work themselves loose. : again, vaseline on the threads or i used plumbers PTFE tape.
Some people use super glue or nail varnish for these problems but it is a more permanent fix and can make future adjustments difficult.
