When Coon Thornton et al took over Parkville and Platte City, the New York Times had a correspondent on the ground there. In an article the Times ran July 28, 1864 at pp. 1-2, they lay out a pretty thorough account of events, and mention Bissett multiple times.
Bissett is first referred to in the story as it discusses the takeover of Parkville, in regard to "eighty men under the joint command of Thornton, Taylor and Bissett, the two latter of Quantrell's murderers...." Thornton being Coon Thornton, and Taylor being Fletch Taylor. The article mentions how the Paw Paw Militia under Ford switched sides and assisted the three men's efforts in taking the town.
The article speaks about the activity in the area. It then says Thornton's command was formed with Thornton being elected colonel, W.L. Kuykendall lieutenant colonel, Thrailkill major, and "Taylor and Bissett commanding the Quantrell companies...."
The lengthy article goes on to speak of the dispersing of the force, stating "the dead were not of the same stripe as Quantrell's. This was accounted for afterward by the fact that Taylor and Bissett, under Maj. Thrailkill, were out on an expedition and made their escape."