All user traffic in bridge mode SSID will be bridged to the local ethernet. It means the traffic sent by client is not forwarded to the controller. The switch will learn the MAC address of the wireless client on the port where AP is connected.
If the controller is not reachable Campus APs will rebootstrap after 8 seconds (default value of bootstrap-threshold in ap-system-profile) and will reboot after 10 attempts. So all SSIDs will stop broadcasting if controller is not reachable.
If the APs are provisioned as Remote APs then there is an option to keep the bridge SSID active even if the controller is down by configuring 'rap-operation' to 'always' in VAP profile. Please refer below link.
https://www.arubanetworks.com/techdocs/ArubaOS_63_Web_Help/Content/ArubaFrameStyles/Remote_AP/Advanced_Configuration_O1.htm