When I split the bin and put new bedding and compost on one side to move the worms along everything else seems to go with them into the new bedding. Once in a while there are a few springtails but they don't seem to hurt the plants.

The other bugs in your bin came from your garden in the first place, so they're unlikely to cause any huge harm. If you want to reduce their numbers, spread your compost out over the soil to dry and watch the birds swoop down for a feast. (Right now I have two robins picking appreciatively at the new raised bed I'm in the middle of making!)