I've installed KVM and set up bridged networking as per the instructions in this user guide.
The guest on the VM seems to be working fine. I can SSH into it and it can ping the outside world. But now the host machine no longer has internet access.
The network manager was reporting that the wired device was not managed. I found this thread describing why it was showing up as not managed and giving instructions on how to make it managed again. Network manager says "device not managed"
So now the wired connection is managed and the network manager even says that it is connected but it doesn't actually have access to the internet.