Does the combat log say Bairdotr is doing poison damage, or are undead just bleeding poison when getting hit by piercing damage, and healing from that.
Do you have the Elemental Ranger damage? That could add extra poison damage to attacks if they are standing in poison.

I tried that bow killing a few townspeople in the harbour, and didn't do any poison damage, just piercing. That was at level 3; with a level 15 Bairdotr from a different playthrough, in the harbour and Silverglen she did piercing damage, and if it wasn't a one hit kill, also shadow damage.