I'm finishing a graduate degree focused on the history of the Canyon area in Yellowstone. The bridge you have shown is called "Canyon Bridge." It spans Jay Creek as it joins the Yellowstone River. It is not part of the Artist Point road.
Chittenden Memorial Bridge spans the Yellowstone River at the start of the Artist Point Road.
Many history books on Yellowstone will corroborate this information (books by Haines, Whittlesey, etc.) as will my thesis which should be finished this fall. It will be downloadable from the Montana State University website.