I have a different approach.  In between trips, with my water tank perhaps
1/3 or so full, I add some clorox to the water.  This of course keeps the
water in there from going stale, but it also chemically "scrubs" the tank
while I drive around.  To make sure and get this in the lines, I run the
faucet for a while, until I'm convinced that clorinated water is emerging.  I'd
feel confident letting this mixture sit in there for quite some time.  

When I'm ready for the next trip, I drain out all the water, either from
underneat or thru the faucet.  Then I fill it, run enough clear water thru
the faucet to make sure the chlorinated is out, and for good measure let
THAT water out.  Then I fill again, and voila! - fresh water, with no
aftertaste, although I confess I'd tend NOT to use tank water if taste
were a top priority.  

I like this system because I don't have to get into the top of the water tank
thru the storage bins, and don't have to worry about drying out the tank,
or what's growing in there.  It does occasionally occur to me to wonder whether
the clorox is bad for the tank or the pipes, but so far, so good.  Comments?

/martha