How to ssh via USB Ethernet adapter
ssh root@[arduinoname].local

does the trick. Just replace [arduinoname] with your board's name: ssh root@myboard.local
Seems to take a minute or two to initialize, so if it doesn't work immediately don't give up right away!
This however won't allow you to access your internet, so I'll still have to connect to my router if I'm going to be downloading anything.