Variable inductor question

Here is the idea - I have a P core ferrite and I wind two coils on a bobbin sitting inside of it, one is the main coil that will pass the signal and the other is a bias coil that I'll feed with DC current from a high impedance source (to avoid transformer effect), the higher the current in the bias winding the stronger the magnetic field, thus the inductor might get saturated earlier. I noted this drops the series inductance of the coil as well but the Q remains the same. How would you suggest to drop the Q other than using wire with higher R or adding an external series resistor?