The circuit breaker has only 2 places to hold wires. There are 3 wires. These are the newest versions with no pig tail. Do I need to wire it to the neutral bar? I thought the idea of this new design was that it didnt have to be wired separately.
There would be no pigtail since the breaker gets supply neutral from the rail. The whole point of a plug-on neutral breaker is that it clips to both the hot and the neutral rail on your breaker panel. That covers two wires; the other two are the usual branch circuit wires that you attach.
If your panel does not have the needed neutral rail, this will not work. It's not the worst breaker mis-spec you can make, but don't make any. You cannot use any random breaker in any random panel, only breakers made for that panel. Get the panel brand, type and model number and ask either right here, or at a real electrical supply house who is an authorized dealer for that panel. Home Depot's shelf stockers will only mislead you.
As it happens, we have a pro here who specs breakers for a living, and can tell you more than I can possibly understand.