I bought a firm bristle toilet bowl brush at the Dollar Tree that works great. With the valve open, I rinse it out, drain, close the valve, then put in clean water from the garden hose, some Dawn, a little bleach, and scrub a dub dub. Open valve, rinse out, you are done.
I saw this Pro on Youtube clean His in a similar manner, works for me.
How I keep my live wells clean - YouTube