This is a tough one, there are many military issue 22 caliber rifles. I have not come across a single shot bolt action except for the Remington 40, but found an Army manual for 6- 22 caliber bolt action training rifles. It has all of the specs, parts break-down and operation manual for the M1922, M1, M2, Remington 513T, Stevens 416-2 and the Winchester 75. A link follows. All are magazine fed, 5 rounds plus 1 in the chamber.
I also found a Springfield M2 Trainers on Guns International, scroll down the page at the following link,
There is also a Remington Model 40X-H1, W/E , Winchester Model 52D, Mossberg 144US,
Mossberg also produced many Training Rifles, but no single shots that I am aware of. The Model 42, 43, 44, 45, and 46 are all extremely accurate, but are either magazine or tube fed bolt actions. I have 1 of each, 2 of the Model 43.
Mauser produced quite a few single shot training / target rifles. The Blue Book lists 8 of them, but no mention of a hexagon or octagon barrel. There are many other Mauser models in 22 LR. Some are listed on the above link to Guns International. They were also produced by Walther and Anschutz.
The Romainian Model 69 is a 5 shot with a round barrel, very accurate too.
CMP lists an Anschutz M1903 single shot 22. I am pretty sure it has a round barrel.
The Remington No. 1 1/2, No. 2, No. 4 and Remington Hepburn No. 3 are all single shot rifles with octagon or round barrels in 22 LR. They are Rolling Blocks, not bolt action.
I hope this helps you,