Sorry for the late reply, I don't get notifications for *New* threads.

Make sure your bonedog has their own inventory of food, or at least accessible (within the "AI" tab of the Squad Menu - "Share Backpacks" option).

It's easier to give the bonedog a backpack and place a stack of cooked meat, etc. so they choose to eat this rather than some random person. You can find these at Farm stores or random nomad traders.

Player owned bonedogs can still do the "fetch" game where they'll chase arms, etc. rolling around, so they might also do that with Prisoners if they're hungry enough lol.