Born William Thompson in Knottingley, Yorkshire, England, immigrating with his family and older brother to the United States as a child. His family settled in Texas, and during the American Civil War both he and his brother volunteered for the Confederate Army. His older brother would go on to fame as a gunman and later as a lawmen and Chief of Police for Austin, Texas. Ben Thompson was more stable than his younger brother, having an even temperament, albeit accompanied by a deadly side if need be. Known as having a violent and quick temper, the younger Billy Thompson often found himself in trouble, usually from violence.
His first known gunfight was on March 31, 1868. That day, while attending a fist fight between a Caucasian man and an African American man, a US soldier named William Burke became upset that the townspeople favored the black man, this being partly because the army were seen by locals as an occupying force following the war. When he lashed out verbally at Billy, the two argued, then later Burke apologized, asking to buy Billy a drink. The two men spent two hours drinking, then went to a bordello together. They argued a couple of times over minor things during their time together, but for the most part they seemed to have gotten along. After they entered the bordello, Billy Thompson went upstairs with a prostitute, and for reasons unknown William Burke again flared his temper against Thompson, and began walking the halls shouting threats against him. Finding the room in which Billy had entered, Burke kicked in the door armed with a pistol, and after the two exchanged shots, Burke fell badly wounded, and died the next day. Feeling he would certainly hang for killing a soldier, Thompson fled.