Idaho Department of Agriculture Needs Science

It is my understanding that brucellosis, a disease that affects humans, bison, cattle, and elk, is transmitted from Bison to other Bison or to other animals such as cattle via contact with fresh afterbirth. This makes it quite possible for Bison with the disease to infect cattle, but only under very specific conditions, but those conditions do not include an adult Bison bull wandering around on ranch land. Nonetheless, "A bull bison was shot to death on Henry’s Lake Flat today, according to Buffalo Field Campaign volunteers and the Fremont County Sheriff’s Department."

The Island Park News notes "...no bull bison has ever transmitted brucellosis to domestic livestock. Brucellosis is a disease that can cause livestock to abort their claves until they develop tolerance for the brucella organism. The organism is most active in the afterbirth of a bison calf for less than 48 hours after the birth. Bison births occur well before domestic cattle are brought to greater Yellowstone for summer grazing." Also, the disease, if it does infect cattle, does not kill them. It might cause them to drop a calf once, but thereafter their immune system adapts. So, brucellosis is not insignificant, but the threat it presents and its consequences are a bit more detailed and nuanced than the "shoot the bison on sight" policy (and I exaggerate only slightly) is not good management or good science.