I have a feeling that Australasian bison are probably pure, as they are all descended from animals gifted by the Canadian government in the early 1900s (1920s/1930s) - but I don't really know the history of hybridisation in American bison.
In 1905, the Bronx Zoo set out to save the species from extinction through captive breeding and the eventual reintroduction of captive-bred animals. The first reintroductions started at the end of 1907 and lasted until roughly 1935. Due to the captive populations being relatively small at the time, some of the animals acquired for the breeding and reintroduction programs were sourced from ranches that bred them for Human consumption. Unbeknownst to the conservationist at the time, some of these bison had been crossbred with Domestic Cattle by the ranchers. These hybrids were thoroughly mixed in with the rest of the population. A study published in 2012 found that pretty much all the reintroduced populations and all of the captive animals in the US at the time had cattle genes present. If I recall correctly, a subsequent study found that these hybrid bison are actually less suited to survival in the wild than pure bison, and on average are killed by predators more often. Pretty much the only pure wild populations are the animals in Yellowstone National Park, and the few herds elsewhere that are directly descended from Yellowstone that were never mixed with other populations.
I personally find it very hard to believe that certain European zoos have managed to maintain pure herds while most others have hybrids when the hybrids have been present in the US population for over 100 years now. When the Bronx program first began, there were only a few hundred bison left in the wild, so it's not as though they would have been readily available for European zoos to import in large quantities and obviously there have been a lot of imports from the impure US population since in order to maintain the European population. The presence of pure herds would have required extremely careful selective breeding from probably a fairly small number of pure bison starting from the late 1800s/early 1900s, which simply would have been impossible considering the impurities weren't widely identified until the 2010s. I'd be happy to be proved wrong, but I really can't see how it's possible unless certain zoos never brought in any additional animals from US imports after 1905 in which case I'd imagine the herds are highly inbred.
All of the above pertains to B. b. bison, have no idea about the history of B. b. athabascae.
~Thylo