| Basses behave in a fairly wide range depending on age, repair condition, soundpost tightness and saddle fit tightness, and things like how recently the lower bouts came loose and were re-glued etc. It's hard to predict how yours might react. I'd suggest playing it safe and removing the post entirely after taking down the strings and bridge. Better to be safer and go through the minor hassle of finding someone to set it up again (if you haven't learned to do this yourself) than to have to suffer serious surgery for a new soundpost crack in the belly. On the saddle fit thing; I've seen a lot of instruments, from violin on up in scale, with serious cracks coming up from the lower belly right along one side or the other of the saddle because these have been fitted tightly and humidity has dropped into the low 30's or lower. There should always be at least a 0.5mm gap on either end of the saddle unless it's a half-saddle, fitted only part way through the belly. The full saddles going right down to the block, when fitted tightly, provide an excellent stress riser, often causing damage. It's hard to find an older bass without such cracks, usually badly repaired. An overly tight fit of the neck mortise in the belly can also cause cracking, but this is more unusual due to the ability of the neck heel to shrink at least at a similar rate to the belly if not quite so much.
You might consider putting a wet sponge into a plastic tub with holes in the lid in your flight case, if there's room and you can prevent it from bouncing around. Something like those 'lock-n-lock' sandwich tubs, Rubbermaid or whatever, are perfect, as you can seal down the lid and easily cut holes into it for water to evaporate at a controlled rate. Just make sure it's not so wet it can drip. More containers with less-wet sponges are better. And then if the humidity where you're going is low, get a cheap room humidifier. There are a few types. Avoid the filter types as the cost and risk of molds are not fun. Spinning or ultra-sonic types are preferable, with no heating, just cool mist. Or go primitive - I used to use a stock pot full of water on a hotplate set to the lowest heat. Stopped the popping and snapping of basses in my house during February cold snaps. Now I use a little Sunbeam impeller humidifier, and though it's a bit loud, it works very well for a 10' x 10' room with lots of instruments in it. | 
