You can buy an annual racing license ($60 for adults; $30 for junior or collegiate) which covers you in all USA Cycling races and expires on December 31.
OR, if you don’t plan to get your money’s worth out of an annual license, you can go one race at a time with one-day-licenses which cost $10 each. These can be purchased on site at the race you choose to enter.
They only have one organization to join though, not two and of course it is only the rider that needs to be a member. Their fees are much cheaper too.
You do have to pay an additional $30 per discipline to have a license to race in say road racing and mountain bike races.