I think the Bryston is both a UPnP player (renderer) and a UPnP server (but the manual is not very clear on that).
JRemote certainly cannot control the Bryston server; it is designed to control the JRiver Media Center server. If you did have JRemote and JRiver MC then those two together can push music to UPnP renderers. So if the Bryston is indeed a renderer, they could push to it. But as the Bryston documentation says you need also an external DAC, that all seems a bit of a waste of time, since MC could drive your DAC directly.
In other words, if you want to go the JRiver route, then buy JRemote, JRiver MC, and a DAC, and ditch the Bryston...