Congratulations on the new Airstream, you're gonna love it!
The Sport Bambi is not among the Airstreams recommend for use of the bike rack by Airstream.
Probably because the frame is lighter than the other models. The risk would be separation of the frame from the shell on uneven roadways, a very difficult repair. Common on some older Airstream models.
I don't think it would be worth the risk. There are other ways to bring the bikes along, we put them in the pickup bed, others on top of the car.