Bi-color LEDs are the same LEDs as uni-color, just there is more than one LED housed in one package. Bi-color LEDs may have two or three leads depending on the intentional connection method.
Three lead LEDs have a common cathode lead to which both LEDs are connected internally.
To tun one of the LEDs or at the same time, connect the cathode to the ground via a current limiting resistor which value is equal to one LED required limiting. Of course, you can connect current limiting resistors to each of the anodes and control current individually. Then you can apply power to one of the anodes or both at the same time to have bi-color amber illumination.
Two leads bi-color LEDs to have two LEDs connected in parallel but opposite sides. One LEDs anode is connected o another LEDS cathode, and the other leads the same way. So by applying power, you will be able to light only one LED. For instance, if you connect to a microcontroller, you will need to use two microcontroller pins to control both LEDs.
So you cant turn on both LEDs at once without specific techniques like dynamic switching both LEDs at high speed that would make the effect of both LEDs lighted on.
If your design has a limited number of pins for controlling bi-color LEDs, you can use an inverter chip to reduce PINs to one and have the ability to control both LEDs, as shown above.