You are really going to chew up your bike if your daily ride is wet and muddy. I would re-think the whole idea if that was going to be the case. But yes, an outdoor hose for the bike and you sounds necessary here. It doesn't need to be a shower, just a hose with a nozzle on it. Then go inside and take a normal shower in your bathroom.

You might also want a dedicated place in your garage to put a wet bike and to hang up wet gear to dry.