Please read the entire FAQ:
http://wiki.linuxmce.org/index.php/FAQUsing wireless links on a network meant to distribute media, which has high bandwidth requirements, automation commands, which have high reliability requirements, and diskless boot images, which have reliability and bandwidth requirements, is a pretty bad idea. You will see this response to every person who has asked about using a wireless link on the network - whether it be a bridge, the Core's primary NIC or the Core's internal NIC. The only devices that will support a wireless link are the Orbiters.
You are, of course, more than welcome to try whatever you like, but I would suggest you go for the wires to save frustration and time.
A single NIC setup is an unsupported configuration. There is a document that describes how to migrate to a 2 NIC setup, though it is probably out of date, so you may have to do some of your own research and trials.
http://wiki.linuxmce.org/index.php/Single_to_Double_NIC