Create Wireless Bridge Connection Between Modem & WNDR3700 Router My ADSL modem is in one room and my Computer (Mac) and Router is in the other. I'd like  the Router to connect to the Modem wirelessly to access Internet.

I've enabled Bridging in the Modem and I'm able to connect to the internet via an ethernet cable after setting up a PPPoE connection (with ISP settings) and connecting directly to my Mac. However, when I try and unplug the cable and even after entering the Internet access settings (username and password) in the Router I'm unable to connect to the Internet wirelessly.

Im using a Netgear WNDR3700 Router and a Technicolor TG582n Modem. My Mac is running OS X Mavericks.

I'm not sure where I'm going wrong!
Nothing is going wrong, this is expected behavior.  You are disconnecting the path used by the router to connect to the modem.  The short answer is, you can not do this this way.  The router needs to be physically connected to the modem if the modem is bridging.

The long answer includes explanations that have to do with the Data Link Layer versus the Networking layer and using the router as a wired to wireless bridge...

If the modem has built in wireless capability you could turn everything on in it.  I do not know if your router will act as a wired to wireless bridge (backwards from the usual).  This would require special configuration that is not what is usually expected.