Thanks for all your help!

When I get home tonight I'll check the voltage accross for 240v. I
didn't do that. At the main panel I connected the black and red to the
2 pole breaker, ground to ground bus, and white to the neutral bus (not
used). I'm thinking I'll find that I don't have 220v. The sub-panel
is not bonded. Could that have anything to do with it? How will I
know where in the panel I can add 220v breakers and where I can't?

I used the 10/3 so that I can change the configuration should my needs
change in the future.