I'm not clear on what you mean when you said "both the BB1 and B2 are referencing the same IP address from the same router." The router assigns a unique IP address to each device on the network. Although it's possible that the B2 could get the same IP address that the BB1 had earlier, the BB1 could not still be on the network with that IP address when the B2 connects. When both are on at the same time, they will have different IP addresses.
The WebUI is the same for each device. I keep two browser windows open, one each for the B2 and BB1. You just have to make sure that the browser window you want for the BB1 is given the correct IP address for the BB1, and similarly for the B2.