Very odd.
If the bar was someone else's left on the taxiway, the ground crew would not have released the aircraft to taxi, or the taxiing crew would have seen it and stopped, so it can't have been that.
Had the bar been left attached to the nose-gear, there is a frangible link that would have broken when they moved forward, releasing the bar and they might then have run over it with their engine. So that would be a ground-crew issue, but also the flight-deck, since they wouldn't have seen the tow-bar attached to the tug to confirm "clear".
Third possibility is that the bar was removed normally and seen as "clear" but it then became detached from the tug and rolled away, coming to rest on the RHS of the aircraft with nobody seeing or realising. Or maybe the ground crew did wave but both pilots were looking forwards by then.
We had an SOP to each have a good proper look round to confirm "clear left" and "clear right" before moving, but on many types, you cannot see your own engines from the flight deck - unless you both laboriously unstrap and stick your heads out of the DV windows.