Bridge mode will disable all routing ability from the SBG8300, so the first device to connect to it will receive the single public IP address that is assigned to you by your ISP. If you would like to continue using the Ethernet ports on your SBG8300, but still avoid having 2 Wi-Fi networks being broadcast, you can disable the just the wireless on your 8300. Doing this however may cause other issues, such as double NAT, since both the 8300 and your new router are now assigning private IP addresses. If you notice strange issues on your network, you can switch back to bridge mode and just use the Ethernet connections from your router, this is usually the best bet anyway. 

Let me tell what is happening, when you enable the bridge mode you are disabling wifi capabilites of the SBG8300 so the gateway will work as a cable modem. So, the SBG will receive the public IP address from your internet service provider, let’s say that is the definition of bridge, so the SBG is getting only one IP and transmitting it to the device that you have connected via ethernet, in this case your router. If you try to use the other ports that is not going to work because only one IP can be used at the time we can say.

There is a protocol called DHCP (dynamic host configuration protocol) this basically assigns IP address to your devices connected to a router, so since we are shuting down the router part of the SBG we are turning off this feature we can say