Ethernet bridge for your xbox?? Why on earth would you pay good money to do such a thing? Unless of course you mean wireless bridge...
Let's start from the basics...
1. The xbox has an integrated Ethernet port. You can use standard Ethernet cables (UTP) with RJ45 jacks on it.
2. Normally you need a hub or switch to connect Ethernet devices with one another using normal "straight" Ethernet cables.
3. You can circumvent the hub or switch necessity using a "crossover" Ethernet cable.

What you need to do:
1. Find a crossover Ethernet cable and connect it to the back of your xbox and your laptop's Ethernet card. If you can't find a crossover cable, use straight cables, each connected to a hub. (If you were talking about WIRELESS network adapter and bridge, skip this part).
2. Boot the computer and xbox and go to your dashboard's "Settings" menu. Under "System Info" or something similar, check for the network config.
It should read something like this:
Use Dynamic IP - no
*or* Use Static IP - yes
IP address: ###.###.###.###
Netmask: ###.###.###.###
You have to make sure that the computer and the xbox have compatible settings.
After you make sure that your xbox has a static IP, most probably something like:
192.168.1.10
with a Netmask of, say 255.255.255.0, change the computer's IP to something like
192.168.1.1 with the same Netmask.
After that, you can ftp to your xbox using its IP and the username/password that are listed under FTP settings.

Hope this helps... Just improvise a little if your default settings are very different from what I've described.
PS. If you find any settings like "Gateway", or DNS ignore them...