Do bear with me as this is just an idea I had on the walk home yesterday, I haven't actually built it yet (and am not very practical minded).
Take one piece of chicken wire, slightly larger than twice the size of your bubble wrap.
Place bubble wrap so it covers one half of chicken wire, with a border of chicken wire.
Fold chicken wire over so it encloses the bubble wrap. Twist the ends of the wire together so it is secure.
Bend whole thing into desired shape.
Make end pieces using same method.
Being very light, you'll probably need to peg it into the ground.
Do you think it'll work? I need chicken wire now!