Just a query....are you sure you are inserting the mounting bushes themselves?
I have just checked all three basses/guitars I have with the three point bridge and none of them are loose in the holes.
The bridge mounts are two piece....and adjustable inner pin with a screw thread...and a bushing with both a socket with vertical splines on the outside to lock into the wood....and a thread in the inside for the pin to screw into.
As in the picture attached....the pin unscrews out of the socket bushing that hammers into the guitar body.