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Ms Davis told the BBC she had run ahead of Mr Bourgeous on the trail when she saw the bison. She passed it once, before deciding to turn around and rejoin Mr Bourgeous.
"I wasn't comfortable standing at the mile marker waiting for him, and I didn't know how comfortable he would be seeing [the bison] too, so I turned back and passed the bison again, giving it as much space as possible."
But when she was on her way back, four cyclists came down the trail and "spooked" it, according to Davis.
The bison charged her and she began running away.
"I looked over my shoulder, seeing it get closer - and I looked again and it was pretty much right behind me. Right as I saw it, I flew up in the air 15ft (4.5m)," Davis told the Washington Post.
She landed on her back and lay completely still - remembering what happened to Mr Bourgeous - as the bison sniffed at her.
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Eventually, it strayed enough for Bourgeous and the other people on the trail to help her.
In hospital, Davis learned that that the bison's horn had gone through her ankle.
The attack happened on an established trail in Antelope Island State Park.
The Independent quotes Bourgeous as saying, "I am not superstitious, but I have this weird feeling they don't like me."
In 2016, researchers reported that about half of attacks by large carnivores - including bears, wolves, coyotes and cougars - on people in North America, Russia and three European countries were the result of "risk-enhancing human behavior."
Mind-blowingly, the most common risks included "parents leaving children unattended" and "approaching a female with young."