It's not routing table. A bridge is L2 device and uses its forwarding table to forward frames to destinations. The L2 forwarding table is made by analyzing various frames it receives through its ports. when a frame comes, it processes that frame's L2 header and records the source mac address M and the port P through which it came, into the forwarding table. when another frame with destination mac address as M comes, it will look up in the table that is already built and will decide that - to reach mac address M, it should go through port P and will forward the frame through P.
you can refer,
1. https://en.wikipedia.org/wiki/Bridging_(networking).
2. https://networkengineering.stackexchange.com/questions/13012/how-does-a-switch-learn-a-switch-table
note: a switch is a similar device as bridge except switch can have multiple ports whereas bridge has two ports. Even though switching is an L2 concept, the switches in the industry now handle both L2 and L3 and are more advanced than their formal definition "multi-port bridges".
