While up in Maine a few weeks ago, I stopped at a LGS and saw a Muzzleloader that I liked. Now aside from buying one locally, my question is does that Gun store have to ship it to my FFL or can they ship directly to me?
The ML is NIB.

Can ship straight to you.  18 and over.

Usually, federal law allows muzzle loading firearms to be purchased accross state lines both over the counter and by shipment, without (federal) paperwork or an FFL required- since muzzle loaders generally do not fall under the GCA definition of a firearm.

Some muzzle loaders ARE GCA act firearms. These are muzzle loaders that were built with a firearm receiver. Examples include the certain Savages, Mossberg Shotguns fitted with muzzle loader barrels, TC Encore and Contender series firearms fitted with muzzle loaders barrels, AR-15 receivers fitted with a muzzle loader barrel/ upper, and the like.

Muzzle loaders usually are not under the auspicies of the NFA. Eg. cannons >.50 are not large bore destructive devices, 20 GA Howdah pistols are not AOW, A chopped down Brown Bess is not an SBS, a stocked Colt 1851/1860 revolver is not an SBR.   A major exemption would be certain concealed firearm AOWs, such as an NAA Companion with a Wallet Holster.

Certain states regulate some or all types of muzzle loaders as conventional firearms. In some ways Connecticut is one of those states. There is no exemption to the definition of a firearm for a muzzle loaders or other antique firearm in Connecticut. I know of cases in which prohibited possessors have been prosecuted for possessing muzzle loaders in Connecticut. However, there are exemptions to the pistol and long gun transfer procedures related to antique pistols/revolvers and long guns (respectively). [I am NOT discussing carrying antique pistols in this thread. That is a very complicated topic for a person who does not have a pistol permit]

Some states not only regulate them as firearms but also regulate their transfer in various ways- which cause sellers in those states to not ship direct. Some states also prevent their residents from directly obtaining muzzle loaders from out of state or require them to obtain and present certain permits first.

Despite being legal, some sellers will not transfer muzzle loaders without paperwork or authorizations out of an abundance of caution. That's their personal business decision.