trying to id a climbing vine. Came up with "Bower vine." But with...
I'm not sure what you're asking. The picture looks like Bower Vine (common name). The latin name is Pandorea jasminoides. Are you looking for the origin or etymology of the word bower?
In Montana we have a vine called "Virgin's Bower", Clematis ligusticafolia. Looks like bower is from old English, "room, hut, dwelling, chamber'. Maybe some vines have common name that includes bower, because vines can cover trellises, or other structures to create a room, or dwellign of sorts.
But maybe I've completely misinterpreted your question. Let me know.