We can nail down Bill and Jim Anderson's first guerrilla outfit with specificity by looking at the February 7, 1863 issue of the Lexington Weekly Union. It refers to it being headed up by "Reed." Sigh--him again without providing a first name. Since it's almost impossible to easily come up with this particular article, I'll run an extract of it in a followup post below.
So we have two possible first names for Reed--William, which was according to O.F. O'Dell in 1899, who had gone off early in the war and joined the Nebraska Cavalry. There is no evidence of a William Reed living in proximity with the Anderson's, and there is no William Reed in the annals of Civil War history as having ever been a border guerrilla, let alone having been associated with any outfits the Andersons rode with.
The other possibility is Jim Reed. In 1886, John Maloy wrote about the Andersons riding with Jim Reed early in the war. Now Maloy didn't mention him by first name, but he did definitively identify him as subsequently marrying Belle Starr. There only being one Reed to whom Belle Starr was married -- Jim -- this pins Maloy's man down as being Jim Reed. And we know said Jim Reed rode with Quantrill, which means Bill Anderson and Jim Reed did ride together. And, unlike the mystery William Reed who never shows up in Border Guerrilla warfare annals, Jim Reed does. Repeatedly. We can prove the existence of 'Jim Reed Anderson Guerrilla Colleague' through multiple contemporary sources. The only mention of 'William Reed Anderson Guerrilla Colleague' was a quick reference to such a name four decades after the fact by a man in Nebraska at the time such association was alleged.
Unless somebody can find me something definitive that a Border guerrilla named William Reed even existed, and can be tied to Bill Anderson, I'm thinking the one candidate known to have actually existed, Jim Reed, is who I'm going to have to go with.