How are you presenting your login credentials?  I assume this means you're using an Active Directory environment.  What's probably happening is that you're using cached credentials when in NAT mode, and when bridged it's trying to validate against your DC.  Try logging in using DOMAIN\username or username@domain (fully qualified domain name) when bridged.  Also, try using other accounts that are in your AD environment to login.

I'm not too familiar with some of these things, but I'll take a stab at guessing.

I wonder if the domain is set up (or even can be setup) to care about the MAC address of the machine from which your user account is trying to log in from.  If so, then it could make sense that NAT works, but not bridged.  When the VM is attempting to authenticate while bridged, it would appear as a new (unknown) machine to the domain controller.  However, with NAT, it would appear as if the host machine were issuing the request.

Now for my guess about the second part.

Once authenticated, I wonder if your domain automatically passes down proxy information to your host.  If so, then while using NAT in the virtual machine, you would need to configure your guest OS's proxy to mimic the configuration on the host.  Using bridged wouldn't present this issue, since incoming traffic is unfiltered on its way to the guest.

If you are on a corporate network, see if you can ask your IT regarding the setup of the domain and proxy configurations.

I've had a simiar issue. I found that the firewall on my host PC was turned on and interfearing with the VMs. In this case it was the Stateful Firewall that comes with Cisco's VPN client. I disabled it by going into the Cisco VPN client and selecting Options-->Stateful Firewall (Always On). You want to clear the checkbox next to this item.