When I get home from a trip I remove the hose from the water blatter, drain the water from the hose, clean the bite valve and stick the hose in the freezer. This keeps all the little nasty's from growing in the hose and does not require a brush to clean out.
I usually just drain and rinse out the bladder and let it air dry. I've never had an issue doing it that way.
I remember reading a tip one time (can't remember where, perhaps on VFTT?) that you can clean a bladder with denture tablets. Fill the bladder with water and insert a couple of tablets. It should be nice and fresh in a short amount of time. I have not tried this method yet.