RC servos can be controlled directly by the PWM outputs. The 3.3v output level of the PWM is enough to control a standard servo. So, just hook up:

 - The black lead to ground on the BeagleBone 

 - The red lead to the positive terminal of your 5-6v power source

 - The white lead directly to one of the PWM outputs.

 - See: Using PWM outputs to control the PWM output and

 - See Pin Muxing for how to control what pin the PWM output is assigned to