Father was #7 non-res bull last year, and he got a tag. I believe the first 50 will get called/offered a tag. I spoke to fish n game and they said not everyone who is issued a tag will buy/take their tag, so if they offer 50 tags say maybe only 20 will use them.

Give jackson,wy fish n game a call though and they'll be able to give you a pretty certain idea, but I think you'll be hunting a bison if you choose to.