Okay, perhaps this is a stupid question, but do shops require a contract to sell a certain brand of bike?

I went into a shop today looking for the Bianchi Volpe.

The store did not carry it but told me they could order it for me. (They are listed as a Bianchi dealer on Bianchi's site).

I also asked if they had any Jamis bikes (I'm also looking into the Aurora), and they told me they didn't carry Jamis and couldn't order it.

Is this how all shops are? Or are stores capable of ordering any bike from any company?

I'm not a bike shop guy, but my understanding is pretty much what you describe. Particularly for the bigger brands, they're going to lock in dealers to carrying their brands & not a lot of competitors. However, some of the smaller brands can be ordered by any bike shop through 3rd party distributors. For example, there are a couple brands carried by QBP, but they don't have Specialized, Trek, Bianchi, etc.

Generally a bike manufacturer will have specific dealers to sell their products retail. These dealers will likely have a protected territory where no other dealer of that brand will be located. If a bike shop is not a dealer for a given brand, then they cannot order one of those bikes from the manufacturer.