No problem. If it breaks down on your trip, you’ll still have the bike to get home with.
Does your owner’s manual have anything to say on the subject?
Personally, I don’t really think you’ll have a problem. I’ve owned several BMWs, some with automatics, and three with only two wheels. Some of the cars have gone over 200K miles with no major driveline issues. That said, I’ve never towed a trailer with any of them. I like Caddyman’s idea of installing an external transmission cooler just to be on the safe side.
Back in the olden days, many households had a car and a trailer. Almost no one had pickup trucks. I know folks who pulled trailers all over the country with six cylinder cars, some with automatics, some not. I even know of an original Model T Ford that had a hitch on the back. I don’t know what they towed, and it couldn’t have been fast, but the fact is they weren’t squeamish about doing it. I know a retired couple who tow a 24’ travel trailer with a Subaru Legacy. They even tow it through the Colorado Rockies. I don’t know what it weighs, but it’s bigger than the car.
I note that the one in this ad http://www.etrailer.com/hitch-2001_BMW_5+Series.htm has a small receiver, and is only rated for 200/2000 lbs. That should handle your bike.
Have a nice trip.