Jacuzzi has a two chemical cleaning procedure. You put part one in the hot water after you are finished...run the thing for a prescribed amount of time, then drain it and replace with cold water, add chemical 2, and repeat. When you are done, you've cleaned the pipes, or purged them of crud. You aren't really emptying them...
WIth my air tub, it isn't anywhere near as messy, since there is no retained water in the passagways (that is the main reason I bought it vs a whirlpool), so it is much less of a factor.
Both of them say you can add a little bleach to help kill things, and I've done that. The rest I've done is just keep the surface clean, but I should probably get some of their cleaner, too.