In the unlikely case that you can't find a motel that will accept your bike, you can also send it to a Kinkos (Federal Express) or a UPS Store in Mobile which will hold it for you. This might be safer than entrusting your kit to a motel (a third party) which doesn't accept bikes in the normal course of doing business.
I rode the UGRR in 2007. The history is interesting, but most of the actual UGRR stuff extant today really only starts when you get to Ohio. In the interim you will have to be satisfied with the Civil War stuff that glorifies the Old South - in a sort of "Gone With the Wind" way. Of course, that's interesting too - especially in light of African American history, which, incidentally, IMHO, is first and foremost American history. The Cincinnati spur and the Freedom Museum are very worthwhile.
I have 4 of the 5 maps and would be happy to send them to you gratis. PM me.