You would be pushing the limit on a F-250 with a fifth wheel. While attaching a motorcycle hitch to the back of the fifth wheel would subtract some weight, not taking it and you could be overweight on the truck due to the 'loaded' pin weight about 200 pounds more than the empty pin weight.
Yes you are within the 11,300 pound towing weight rating, as your 'loaded' trailer weight will be less than 10,000 pounds - most likely, except with the motorcycle on board will be near 11,000.
However do realize that Ford rated the truck to tow 11,300 pounds while only one driver is on board, so no passengers, they will have to come out of the 11,300 pound rating. So if the GCVWR is say 18,300 pounds and the truck is more than 7,000 with passengers (before hitching up) then the amount over the 7,000 must be subtracted from the 18,300 to get your overall total - still under 18,300 (or whatever is listed in the towing guide.)
Ford towing guides - click and select a gear.
http://www.fleet.ford.com/towing-guides/ How about clicking on 'Toy Hauler' forum, and looking at the toy haulers where you might find a RV that can haul the motorcycle safely, and be towed by the F-250. There are dozens of RV's out there. Most are listed on the toyhauler forum, so click on one of the top posts that says "Complete list of Toyhaulers"
Good luck!
Fred.