i've heard from a lot of bari players that they simply buy an extra ticket and put it in the seat next to them. And don't upfront listen to the gate people...I had Delta tell me I needed to check my tenor, but it fit in the overhead, and even one time where I barely made the flight and the overheads were full, the flight attendant let me put it in the closet on board...just do your best to remain polite at all times....it's not their fault if they don't realize how important our instruments are to us...