The official answer is that the car is incapable of towing ANYTHING. I'd imagine this is due to body/chassis design. My Ranger weighs 100 pounds more than my Crossfire and has less braking and 1/3 less horsepower, yet it is rated to pull up to 1200 pounds and I've pulled 2050 pounds several times (this did not go well, 155 horsepower was not nearly enough).

And do not forget: The maximum load is 415 pounds of passengers and cargo. That means if you, your spouse and your luggage/tools weigh over 415 pounds, you are already exceeding the 'safe limits' of the car and should be ashamed and banned from this site, right? Given that, why not try? Get someone to make a hitch capable of attaching to the car AND pulling what must be about 2000 pounds of bike and trailer and just GO.

Of course, if you get under the car and look, you will be hard pressed to figure out how to pull 2000 pounds. Several forum members have pulled light trailers that, in one case, held four track tires and wheels. Total weight was perhaps 350 pounds. I don't think you can get away with installing a hitch heavy enough to do what you want to do, but I'd like to see someone TRY. It's going to look stupid, and you won't have a lot of ground clearance - but that does not mean you can't do it, just that you probably won't like the outcome and that you'd want to remove it after the trip.

You mentioned cost - this will be a LOT of custom work and probably involve a waiver of liability for the person who builds and installs the hitch - this is not going to be the cheap way out. And from my experience with the 2000 pounds of bike and trailer with the Ranger, I'd suggest you will want electric trailer brakes. I know that sounds like overkill, but I had to really be defensive with the truck. It took as long to stop as it did to get moving, and that trailer had an automatic brake system.

If you read this far, I think you have your answer.