If I restore factory settings will I lose all the data currently on there?
No, data on the hard drive is not affected at all. The only way you would lose your data was if you performed a completely separate and deliberate "Erase Disk" operation.
Also I've read something about bridge mode - could this be a possible solution?
When you set up the TC again, the configuration "wizard" takes care of things like this automatically, so you don't have to worry about what settings to choose. It's all automatic. Post back if you need a few tips on how to get things working again.