Okay so no, poison damage will NOT count in Bide's damage count.
If this attack is successful and isn't already in effect, the effect begins and X is set to 0. During effect, user uses this attack during each of its turns and can't take any other action, and whenever a non-user hits the user with a damaging attack, the HP lost by user due to that attack is added to X. At user's second turn after this one, deals X times 2 damage to the Pokémon at the position of the last non-user that hit the user with a damaging attack during this attack's effect, or if there is no such Pokémon, to one of the opposing Pokémon chosen at random, and this effect ends. Not affected by type immunities. Returned attack is considered an attack by the user. If, during effect, user is prevented from using this attack or isn't active, or when user falls asleep or becomes frozen, effect ends without returning an attack.