We have matress covers that we wash regularly too. But you should still clean it regularly because of the dust mites etc. You should also flip the mattress every few months to prolong its life.
First vacuum it. Then mix a mild detergent with water until it gets suds on top. Then get a towel and get the suds on there (try not to make it very wet) and clean the mattress. Then get some clean water with a little dettol in it put a sponge in it, wring the sponge really well and go over the mattress again. Basically the mattress should only get damp on the surface, don’t let it absorb water.
This is best done in the summer on a hot day when you can open the windows and let it dry easily.