very unlikely you can use the 360 to bridge the gap.
havent seen an option in the settings to set that up but others out there might know a way.
yeah, powerline networking might be the best option for you in this case, if speed is not an issue.
another might be to get a wireless N bridge, so if you add more devices to your tv setup (ps3, wii, etc) then you can get those onto wireless N as well.
if your not thinking about adding more stuff then the homeplug kits would be suitable.
for example, my brother (mpeyper, he'll probably post soon on this topic anyway) has just got a bridge for his lounge, as he has a ps3, old 360, and wii that he wants to connect to wireless N (he needs N for wireless HD media streaming).
he bought a Linksys WRT320N
which he is going to install ww-drt
this is going to give him a lot of flexibility in the future, fastest speeds (wireless N and gigabit) and its relatively cheap (believe he got it for just over the $100 mark).