Just pour a little thinner in the jar and swirl it around to get the paint out of the jar, then spray it through the airbrush. Repeat with some clean thinner and finish up by blowing some air through the brush. That will clean the bottle, tube, and the brush itself and it only takes a minute or two.
There are several ideas around here for "Catch Cans".
Swanny's use of a respirator filter cartridge is probably one of the better ones. I use MikeV's idea of a coffee can, furnace filter, and some PVC tubing. I'll make a sketch of it later if you need one.