I would agree with Matthew, rent a car that can fit your bike inside it – quick, easy and safe. I don’t think a suction cup carrier sounds like a good idea. If it fails it can get quite expensive.
Hygglo.no and Finn.no are websites where you can rent from private parties, but I’m not sure if it’s possible to sign up without a Norwegian phone number.
This one looks like a good option if a station wagon/van is not available to rent: https://www.finn.no/bap/forsale/ad.html?finnkode=338357449