well first to tell i have no banana outside.. so i just my thoughts abut it..
you can couver the p-stem (mother and pup) with leafs or any other stuff to prevent the pup from freezing. basjoo is to my knowledge very cold hardy (-20°C) but i have no proof for the number. Anyway it should survive frost..
if you can buy a basjoo for next year you can try to just leave it. if not or if you dont want to buy a new one you can try cut the pup. but it could also die during the winter inside
the whole plant seems to be "small" and i think small enough to dig out and place it inside over the winter. repotting/planting allways shocks the banana so id say for now its save outhside. if you couver it good the pup should make it
hope my thoughts may help
