Much of this episode is told in flashback; the "present" begins with Brisco and Bowler pursued and captured by US Cavalry troops (led by ex-Pittsburgh Steeler Terry Bradshaw, who in this episode does very well in a strictly dramatic role; not so well in the following episode.)
Charged with treason, the trial continues in the "present", while what brought them to be charged with treason is told in flashbacks.
Brisco and Bowler were sent by President Cleveland in an unofficial capacity to save Jennifer Hart, the daughter of a newspaper magnate, who has been apparently been kidnapped by a Mexican bandit, Carlos Falco. Collecting Pete Hutter (via a presidential pardon), Sheriff Aaron Viva (still Elvis'ing it up), Professor Wickwire and Whip Morgan, Brisco and Bowler head for Pico Blanco, Falco's hideout.
Once they arrive and begin the rescue, they discover that Miss Hart is with Falco by choice, and that she hadn't been kidnapped at all. Rather than try and figure out how they've been doublecrossed, they decide to rescue her anyway and sort it all out later. With many explosions, they succeed.
Jennifer Hart, on the way back to the US, tells Brisco and Bowler that the doublecross has been engineered by General Quarry, a Custer-like megalomaniac who hopes to precipitate a war with Mexico, and make himself presidential-caliber material being a hero in his own war.
Brisco and Bowler decide (once they return Miss Hart to General Quarry's camp) to help reunite her with Falco, and delay the troops who hope to entrap Falco when he crosses the border to rescue the girl, who he doesn't know is being returned to him by Bowler and Brisco (its a little complicated.)
Back in the "present", it becomes clear that Brisco and Bowler are going to be railroaded by General Quarry to cover up his own machinations. He packs the military courtmartial (and liberally interprets military regulations to be able to courtmartial Brisco and Bowler at all), which returns a guilty verdict.
The next morning, Brisco and Bowler are taken out and shot (well, apparently...) in a scene very reminiscent of the execution scene from "Breaker Morant".
Nice time-passing dissolve just before the verdict.