OK, here's most of the basic kit issued with British Land Pattern Arms. (No bayonet scabbard, though.) As you look at the picture, to the right of the Cartouche (Cartridge) Box, is the issue bayonet FROG that remained unchanged from before the FIW to slightly after your period. This held the bayonet scabbard.
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Below is an excellent reproduction made by Najecki, except he uses brass or copper rivets and burs instead of the original ones made of Iron.
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Waistbelt Frog- for use with the above 1" waistbelt. This black leather frog with copper rivets is pictured in Don Troiani's
Soldiers in America book, page 4. Four examples are known to me, including those at Fort Ligonier and Old Fort Niagara. The slot for the bayonet scabbard hook will be on the exterior of the frog (¾" from the top) unless you specify a different location such as the frog interior for an inward facing bayonet, or further down the frog. Overall dimensions: 3" wide by 7 ½" tall. $25.00
http://www.najecki.com/repro/pouches/BritishCartBox.html#waistbelt
That price is very, VERY difficult to meet, even if you did it yourself, BUT you MUST measure your bayonet with scabbard on it to get a proper fit AND you must add a bayonet Locket to your bayonet scabbard.
Now here is something I want to add that should be very important. Though these bayonet frogs were military issue with the Regular British Regiments, there is no documentation of which I am aware that they were commonly used by even a simple majority of American Militia. Some individual militia members may have had them and perhaps even some few militias made up of more wealthy civilians, but the expense of these and for most of the American Militia's, they really had no use for them outside of their drill meetings to go to that expense to procure them. A simpler version of these or even an over the shoulder strap and frog combination, may and probably were more common. I will get into those in my next post.
Gus