yeah but I don't want to wash two pieces of fabric every single time I take a shower
You don't have to wash it every single time. For starters you soak it in soap each shower so it shouldn't get too nasty. You should also rinse it off in the shower when you're done with it in order to remove the dirt it's taken from your body. And finally, if you have a properly ventilated bathroom and you wring it out when done it should dry quite quickly and therefore not get musty.
You should be able to go quite a few showers without washing it.