Dedicating a NIC to a guest was fairly easy.
- Add the NIC to the system.
- Go into Windows network adapters and unbind TCP/IP (both 4 and 6) from the new NIC.
- Go into VMWare Player settings for the guest VM.
- Select Bridged networking and click the button to make the bridge use only the new NIC.
- Start the guest VM; the (bridged) NIC should just work as expected.
I was also able to connect to my VPN in the guest with the dedicated NIC, without any problems. 