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.