So if you send them a check and own the bike they have no right to say that you can't ship it. That is like a person on ebay, I would make that argument with them that as the rightfull owner you can have things shipped wherever you wanted them. This may squeak by, I would talk with the bike shop again.

HERE MAY BE A WAY AROUND IT - ask the bike shop after the sale to please box your item then ask for dimensions and weight, go to www.ups.com or www.usps.com and create a prepaid shipping label that is paid for by you the shipper (to be shipped from the shop to your house) and then send that to the bike shop to put on the box. They are not shipping that item it is you who is doing the shipping and if you paid for the bike you are the owner as well. This could be the loophole you are looking for.