You CANNOT stop them from splashing.
I used to have a bath bowl in the cage, but they would splash water all over the cage and whatever was within 4 or 5 feet of the cage.
Now I use an outside hanging bath. The only opening faces back into the cage. That limits the water they can splash to what they can splash out the opening and keeps the water off the floor.
I have the PlennPlax bath in the pix. Do NOT get this one. There is a design defect where water that is splashed onto the clear top half when it drains down, will leak out and drip onto the floor.

I fixed mine by putting a drip sill of epoxy along the bottom of the clear top half. That much epoxy for 4 baths was not cheap.
Unfortunately I was not pleased with the other baths that I did see at the pet shops either.
As for the cage, 3 of mine are made of coroplast and the back of the cage is coroplast, so the water stays in the cage. The other cage has a sheet of Home Depot plastic sheeting on the 2 sides and back, which keeps the water and poop in the cage.