Do you have to pay both ASCAP and BMI?

To publicly perform music, either live or recorded, you need permission from the copyright holder. The easiest way to do this is to get a blanket license from the performing rights organizations, one of which is ASCAP.

As a composer or songwriter, there's no requirement to join a performing rights organization, but it's considerably easier than trying to handle all the royalty paperwork yourself--if you had a hit on your hands, would you really want to have to license every radio station, restaurant, and roller rink in the country?

ASCAP in particular also has support and education programs for new artists, which many find invaluable for networking.