Selecting which Ring Bridge from multiple echo devices

So i have been successfully using the Ring Bridge on my Echo Gen4 (not the dot, the full blown echo). Everything works fine, but I would like to use the bridge in my new echo show 15, as it is more centrally located, and should solve an intermittent problem with my ring mailbox sensor.how do i go about switching which bridge i use? You are only allowed one bridge per household, and i have already used the one on the echo.I could unplug the echo, unregister all the ring smart lighting, and mailbox sensor, and then try to re-add them, hoping it sees the echo show bridge. But I thought I would ask here before I cause myself a large headache.