Kirby there is a 1863 draft registration for a James M Bissett, native of Canada, in Clay county.
[James M Bissett]
Birth Year: abt 1837
Place of Birth: Canada
Age on 1 July 1863: 26
Marital Status: Unmarried (Single)
Residence: Liberty, Clay, Missouri
Congressional District: 6th
Following this I find the entry below on pg 247 in the History of Clay County. Given the info there I can't help but believe these are one and the same you are looking for.
"About the 1st of June four bushwhackers — said to have been Chas. F. Taylor, Arch. Clements, Peyton Long and James Bissett — drew the first blood in Clay county. Long and Bissett had their homes here. Chas. F. Taylor (or " Fletch " Taylor, as he is commonly called) was from Impendence, and Clements, the cruelest, most desperate guerrilla of the war, was from Johnson county. Fletch. Taylor was the leader. June 5 these four, all dressed in Federal uniform, came to the house of Bradley Y. Bond, a quiet, reputable citizen of this county, called him out and shot him. Mr. Bond had been in the Federal service in 1862, but was taken prisoner at Lone Jack, paroled, and had been at home subsequently."
JEN in Noted Guerrillas on page 244-245 describes your fight and names names.
"Three days after this brilliant episode, James Bissett, John Wilson, Harvey Brown, Thomas Fulton, and Sandy McMacane, camped together in a stretch of timber, were surrounded by two
hundred Federals. Bissett was from Clay county, Fulton and Brown from Platte, Wilson from Jackson, and McMacane from Louisiana. Those who died at Thermopylae were not braver.
The first Federal volley killed all their horses and shot down Bissett and Brown. They crawled each to a tree and fought there until the final rush came which finished them surely.
Fulton, a man of powerful voice, cried out every now and then: "Boys, who's killed?" Once or twice he was answered: "No one yet; but the end is here." Presently Wilson did not
reply. A carbine ball entered an eye, crashed through the brain, and killed him as he stood, pistol in hand and shooting. After his fifth wound Fulton shouted for the last time in the
fullness of his once magnificent voice : "Good-bye to all of you; I go but a little ways in advance!" Then McMacane, alone with the dead, fell first to his knees and next upon his face ;
then there was a great silence. The woods no longer offered any resistance save protest such as any corpse might make. Rushing from every quarter, and infuriated at a resistance which
had cost them thirteen in killed and twenty-one in wounded, the Federals fired round after round into the already riddled bodies and scalped them afterwards to a man."
JEN also state James Bissett was a recruit of Frank James. pg 356.
All told I think but can't prove with primary documentation that "Capt. Bissett" was James Nelson Bissett b 11 Mar 1836, Ontario Canada, son of David Bissett and Eunice McCraney Bissett, d Sept 1864 Howard County.
From the list of Soldiers of Price's raid pg 87 https://mostateparks.com/sites/mostateparks/files/Confederates%20A%20%26%20B%20of%20Prices%20Raid%20updated%202015.pdf
the following tidbit arises :
"Bisset, James Guerrilla Anderson KIA 28 Oct 1864 Fayette MO
Bissett, James Platte City Guerrila Units Bissett's Company From Article Confederate Veteran Vol 30 (1922) page 255 & 277 https://ia800604.us.archive.org/10/items/confederateveter301922/confederateveter301922.pdf
"FIGHTING IN THE WEST.
BY W. H. PATTERSON, SMITHVILLE, MO.
In the summer of 1864, within the Union lines at Platte
City, Mo., five companies of cavalry were organized for Price's army. These companies were made up principally of boys, about three hundred in all. We were mounted on good horses and were well armed. There was plenty of ammunition and guns at Platte City. These boys were all sworn in the service for three years, or during the war. First came Jim Bissett's company; second, Cap Annibus's (sic) company; third, Bill Downing's company; fourth, Fletch Taylor's company; fifth, Coon Thornton's company—all five companies being under Major Thrailkill. We were expecting the enemy to attack us at any time, as there were at least 4,000 Union soldiers on our trail. We were ordered to fall in line and mount our horses, and told that we were bound for Iowa, that we would have soldiers to
fight both going and coming, and if there was a man in the command who did not wish to go, to ride out. But all hollered "Iowa" and we moved out, with a beautiful silk flag presented by the ladies of Platte City. Johnson Barbee, our flag bearer, was in Thornton's company, and, in a battle the next day, Barbee lost the flag and his horse too. Moving north we reached Cameron the next day, traveling
all night. Sending Peyton Long in as a spy, he reported the town well fortified and full of Union soldiers. Our flag, which we prized so highly, having it in our possession only one night
(Continued on page 277.)
....and there I get stuck because all the online images seem to stop at pg 276 though clearly there was more....
But clearly Bissett was in command of a company thus the rank Captain and organized that company at Platte City thus the OR entry "from Platte County"
Hope this helps, not as clean as I'd like but at least we know a bit more. - JJR