They get stuck in the bath because as they make their way around the house, they wander around the rim of the bath, slip in, and can't climb out again. They do not, contrary to the popular myth, climb up plugholes - a spider is far too fussy to go near a dirty plughole, and there is the small matter of the 's' bend which is full of water.
You should not put a spider outside - these are house spiders, and will not survive long outside. They are used to living in the warm, and living off the flies that would otherwise spread around your home. If you don't like to catch them, leave a towel over the edge of the bath, with the hem reaching the bottom, the spider will climb out and be on his way.