Update:
I solved it by following the steps in the linked blog post:
blog.credera.com/.../using-your-windows-8-wireless-connection-inside-hyper-v
My initial instinct was to create an External Network Switch to connect to the outside world. Right? Wrong. Create an Internal one. Then ensure that your Wi-Fi network connection allows Internet connection sharing!
Microsoft could make it a bit more user friendly. Most people aren't going to know the difference between a NIC\Network Adapter\Virtual Switch and a Partridge in a Pear Tree.