Good timing, I just found what I think is the actual species name for this plant a few days ago when I was searching for something else. It appears as though this plant is still a Melastomataceae, not of the genus Bertolonia, rather it is Clidemia hirta. I was a little surprised to find that it is considered an extremely invasive species in tropical areas, considering it is somewhat difficult to propagate from unrooted cuttings. This page describes its natural history and invasive attributes fairly well. Didn't know it could develop vine-like growth, but it probably requires space and maturity for that.
I second the Clidemia spp. I had been growing that for many years and aways had thought it was a Clidemia, as it usually grew to a height of several feet in a matter of months. However, recently many people have been growing something under the name Bertolonia sp. 'Itatiaia', and all photos look similar. I would say that most of these are definately Clidemia if they grow past a foot or two. Clidemia is a tall, fast growing streamside weed. Mine right now is at least 24" tall. I've never had any Bertolonia grow fast or tall, actually it usually craps out on me.