On a singular target, burst damage should always hit. This is not the case with the Bed Crossbow and I suspect it plays a large part in making it feel underwhelming. It seems to randomly miss shots quite often, and this is discounting the missed shots when trying to pierce and army.
The result is effectively a unit that is half of the time half as effective as a regular Springald.
Here is video proof. For reference, this is a Feudal unupgraded Bed Crossbow that deals 7 damage per shot, reduced to 3 by the Boar’s armour then doubled to 6 if both successfully hit. As you can see, this does not happen most of the time, or sometimes, at all.
Side note: the shooting animation is not in sync with the missile. The Bed Crossbow animates recoil and plays the sound a few milliseconds before the missiles leave its barrel.