I've had plenty of car and motorcycle calipers do the same thing over the years. I doubt that bleeding, in and of itself, would make a difference.
It sounds like your pistons are corroded, which causes friction/interference with the seals. You may be able to pull the pistons out of the caliper, remove the corrosion with very fine sandpaper, install new seals (or maybe the old ones), and put them back together (and change the fluid in the process).
The difference with your car brakes is, in my opinion, that they get hot enough in regular use to evaporate most of the moisture, and they are pretty well shielded in any case.
If it's otherwise practical, using an air compressor to blow out the moisture after riding in the rain, etc. is a decent way to ward off this problem. The same is true with chains. I've done so, with good results, on all kinds of bikes and other equipment. Also, the Avid bleed kit works pretty well.