From a look at the code, cave spiders aren't affected by poison, nor are regular spiders. Cave spiders do not have the NBT required for them to target arbitrary mobs; they can only target players, so they would not be able to fight against the bees.
Bees are affected by poison, though like any other mob, they only get down to half a heart. They deal 1 heart of damage for their initial attack, so you'd need six bees to kill a spider.
For these reasons, bees would win as long as they outnumber the spiders by at least 6x, and any less would result in a stalemate.