Commercial worm farms are built up and have a tray underneath to catch the liquid. I don't have one -- I just use a compost bin which is open at the bottom.

Add a lot more bedding. Add it on top, and add dry, no need to moisten if the main worm-space is too damp.

See if the local pet store will give you the used bedding from their small animals cages. I got a bag when they still used saw dust pellets. They now use recycled paper product and is a good absorbant.