The common anode of the LED is connected to 3.3V. The three outputs to control the brightness of the red, green and blue channels are connected to sockets P8_13, P8_19 and P9_14 of the BBB.
The pins are numbered left to right, 1, 2 then on the next row down 3,4 etc. You can also use the pin P9_16 for PWM output.
You can find out about all the pins available on the P8 and P9 connecters down each side of the BBB here: http://stuffwemade.net/hwio/beaglebone-pin-reference/