Here's a good article you may find useful: Bridge versus Router Mode Differences, Advantages and Applications.
Basically, bridge mode set your router's networking to Layer 2:
In other words, what goes in goes out and vice-versa. No IP foot print or coloring.Bridges operate at the Data Link Layer (level 2) and do not understand anything about any communications protocol other than the physical medium (MAC), which is typically an Ethernet.
P.S.: another way to access your router set in bridge mode would be to create a VLAN and the proper route on the router itself. This would be possible only if the router's firmware allows that functionality (for instance Tomato and DD-WRT do). Another way would be to enable your ethernet interface and setting manually as described in post #5.