If it’s a Fender traditional bridge. To keep it stable and from migrating side to side you need to lower the outside part of the saddle on the E and G string. This puts them at an angle causes the saddles to push together keeping them from moving.I've definitely swapped bridges before, and I'd be open to doing it again. I do like how this bass looks with the original bridge, but it is also not necessarily the greatest piece of kit Leo ever invented. Even if I lock down the action, the saddles also migrate side-to-side a bit.
I don’t know if this picture is clear enough, but this is how to set them…

