Me too... forgot to get around to it.
Yeah so it seems historically catch dogs and bears went hand in hand, and catch dog usage on bears was even still pretty common in the 20th century.
Even though it's a fictional movie, and the bear itself is likely a captive "animal actor", the dogs in this scene from the Yearling (1946) I'm sure are a real bear hunting team-
It would just be the most practical way to source dogs for such a scene, and they seem to known what they are doing. When filmmakers wanted a scene where a wild animal is hunted by dogs they would find a guy who hunts said animal with dogs and employ his services.
It's no different really to the dog team used to capture the jaguar in this film-
The jaguar might be a captive jaguar and it might be staged (I strongly suspect so), the dogs however think it's real and really are clearly big cat hunting dogs (maybe normally mountain lion hunters). They've got in contact with a guy who hunts big cats with dogs and to make their video so even though it may not be a real hunt, it shows you how a real hunt works fairly faithfully.
The bear video is more chopped and edited and I think that's specifically to tell the story of it getting away, it wouldn't have in real life.
These videos are fairly consistent with descriptions written by people like Theodore Roosevelt in the late 1800s early 1900s, and also big game hunters like Samuel White Baker and George P Sanderson. The rag tag band of hounds and then either some half-bred seizers, or straight up bulldogs or bull terriers in tow for "fighting" the game. George P Sanderson specifically writes about using bull terriers for bears, and indeed says ALL animals except for tigers can be hunted well with bull terriers.
Thirteen years among the wild beasts of IndiaCombine this with the artworks and accounts depicting the use of catchdogs on bears through the middle ages and back into ancient times, it's clear catch dogs are very useful on bears.
And yet, the practice is largely out of favour or very hard to come across among modern hunters.
North American houndsmen seem very conservative in their approach, and if you listen to them they will tell you that no catch dog can even catch even a hog without being killed. They are clearly way way too cautious so with that in mind I guess it's little wonder they have moved away from catching bears with bulldogs and similar. Maybe some hillbillies are still doing it, but I don't tend to encounter them on the internet. The closest I have seen in modern times is a rough cur or two with bitey inclinations worrying bears that are bayed by hounds, airedales and jagds often feature here, maybe even a rough BMC. I think this has more to do with these guys not wanting to use knives, and being gun obsessed, rather than dogs not being useful for bears. Like I said, all the evidence shouts loudly from the rooftops that catch dogs go with bears like peanut butter and jelly. I have actually myself totally underestimated how well catch dogs can work on bears in the past.
I will say, anecdotally, I knew a guy on molosserdogs way back in the day who claimed his bandog was killed by a bear it attacked while hiking. Otherwise bear performance against gripping dogs that I have seen has not been great.