Bridged mode exposes 2 mac addresses coming out of your ethernet card to the wire - that of your mac, and a separate one for your VM. As far as your network/modem is concerned, your computer looks like a hub/switch with 2 machiens connected to it. The benefit is that you can have 2 separate IPs and not worry about port forwarding, etc. for your VM.
Shared mode makes your mac act like a router, and as such only 1 mac address is exposed to the outside world.
The likely reason for the failure mode during bridged mode is that many DSL/Cable modems will only talk to 1 mac address on the client side at a time. When you have 2 addresses showing (as with bridged mode), only the first one to talk (your mac) get to talk at all.
Unless you have a very specific need for bridged mode (e.g. you are testing DHCP, running a server, etc) in XP, shared mode should work fine for you.