I used to work at a uhaul rental, but it wasn't a UHAUl center, it was a store that also rented. There is a specific trailer for motorcycles referred to as a motorcycle trailer. You'll probably have to go to a UHAUL center for one as opposed to a business that also rents uhauls.
I think they also have a couple of open trailer models for ATV's and things that would probably work. If you go to the UHAUl website, they have a rundown of what trailers you can rent.
I would make a reservation as soon as you know what you want, and be sure to specify where you're picking it up. UHAUL was terrible about moving people's reservations to other locations if they had a bigger ($) reservation for something. For example, if someone wanted to rent a truck for a day, UHAUL would not honor their reservation if another person called later and said they need a truck to take to Florida (those rentals are big $). So often, the in-town customer would have to go somewhere else to pick up their truck.
Good luck,
JB