The one sure way to be legally in the clear is to obtain permission from the copyright holder or their legal representative. In this case we are talking about the American Society of Composers, Authors, and Publishers (ASCAP) or Broadcast Music Incorporated (BMI). ASCAP represents over 575,000 artists that includes a catalog of millions of songs. BMI does not make their numbers as public, but they are almost as large. An artist can only be a member of one of these groups at any given time, so it could be necessary to get a license from both depending on your selections.
Most of the time when a business owner or entrepreneur hears the term "licensing fee". They get out the check book and get ready to take one in the shorts. This would be true if you are dealing with federal agencies, your local county office, or the DMV. Thankfully, as daunting as all this sounds, the fees are not too unreasonable. For example: If you put on an event and obtain a license from ASCAP when all your proceeds go to charity and you have less than 5,500 attendees, then the one-day fee is only $10! If you do generate some profit and not all of your proceeds are donated then the fee would be $102. BMI's rate structure is a tad more expensive, but offers a sliding scale similar to ASCAP's. Below are direct links to the licensing pages on the respective websites. Look for the complete fee schedules under the category for Endurance/Racing Events.
What are the odds that BMI or ASCAP is going to come down on an individual putting on a few small events to make some money on the side? Pretty darn slim, but the price of a license is significantly less than if some suit in New York City decides that your event is the perfect case to "set an example". So cover this one additional detail properly and you can enjoy the festivities at the post race party with no worries!