Does a bias resistor determine the forward voltage drop across an LED?
If you want 5mA then there is 2.0V over the LED, and you can calculate resistance based on the current and voltage that is over the resistor. If you want 20mA then same applies but there just is 2.2V over LED so there is less voltage over the resistor.

So basically yes, bias resistor determines forward voltage. By changing the resistor, current changes, which also changes forward voltage over LED.