The TimeCapsule allows enabling the Guest Network while in bridge mode, but because bridge mode disables all management services, the Time Capsule has no ability to offer any services for this second SSID such as DHCP —± connecting to the Guest SSID will get "No Internet" status on the client.
To address this issue, Apple tags all packets going to/from the Guest Network with the 802.11q VLAN tag ID 1003. This allows these packets to be treated separate from the default Primary VLAN ID of 1. On your main router you will need to create an allocation for VLAN ID 1003 t as well as ingress/egress rules for it.
Once the main router is configured to correctly handle packets tagged with VLAN 1003, it will correctly interpret the 802.11q VLAN tagged packets coming from the Time Capsule and be able to address them accordingly as their own virtual LAN, allowing access for devices connecting to the Guest WiFI SSID.