I think ynot is talking about the fact that; one, yeah washing upside down and not having soil go everywhere must mean it's root bound, and time for a repot. And two; washing in the tub would mean that soil "WILL" go into the drain, if you want to redo the pipes in the bathroom cuz they get clogged up with soil then by all means...go ahead

. Other wise, submerge the plant in a big enough bucket to cover the soil (but not the whole tree) for about 15mins or until the bubbles stop coming out.
If your going to wash the leaves just a simple straight down from the top should do. Whatever is in the leaves is, more than likely, already in the soil. No sence in avoiding whats already there. But a sidelike spray will do too. Just don't "power wash it" give it a "gentle shower" (thats a setting on most garden hose attachments). That should do fine.
P.s. I've never heard of cat spit being deadly to branches and stuff. I would think that if the cat chewed it...the chewing part does the damage that kills. Although on the other hand....It's something that "could" be true. GL- matt