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