Most people using Bridge Mode seem to do that in order to be able to have more control over the networks' behaviour. Lots of ISP's send out modems on which you can not open ports. Another popular reason to use Bridge Mode is that many modems work a lot faster in Bridge Mode than they do in Router Mode.

The setup would something along the lines of two devices:
1. The modem/router you received from your ISP, (WAN), connected to the signal socket in your house.
2. The router you bought extra, connected to the WAN port of 1.

Only 1. needs to be put in Bridge Mode and as soon as you do that, 1. should have only a single working WAN port. In theory this WAN port should allow connections to all your virtual ports. Before you connect device 2. it's usefull to make sure device 2. has gotten a static IP address.

2. Connects to the WAN port of 1. On 2. you will need to configure the ports you want opened and any other aspect you may need. Normally the dhcp server should be switched on to allow device 2. to give out automatic IP adddresses to your PC's, phones and what not.

Bridge Mode and a Repeater are two different things, afaik, even though practically, they may provide you the same service: an extended network. But the repeater simply takes an existing signal and boosts it up so it's range get extended (more or less). Bridge Mode in combination with an extra router gives you an Acccess Point.