Cox WiFi enabled in gateway mode?

I have a CGM4331 Panoramic modem/router with 1Gbps speed, and I manually disabled the Cox WiFi feature to prevent outside people from slowing down my internet by using my router for internet access. Recently I bought a more capable router that will better accommodate multiple devices and enabled bridge mode, does that re-enable the Cox WiFi hotspot for Cox customers? There is no way for me to tell if the one I see in my available WiFi list is coming from my modem because majority of people in my area use Cox so it could be one of my neighbors' modem.