How to determine angle of bank caused by shift in centre of gravity in an aircraft?
You can't. Aircraft are not stable in roll!

Once there is an offset between the centre of gravity and the lift action line, there will be a rolling moment until the aircraft is banked at 90°, at which points the forces become perpendicular, so they can't generate any moment.

The moment will cause roll acceleration, but as the wing going down will have higher angle of attack, its lift will increase, causing opposing moment that will stabilize the aircraft at some roll rate. Which will slowly decrease as the moment between lift and gravity decreases with the increasing bank. But it will not vanish until 90° bank, so the aircraft keep rolling and end in a graveyard spiral.

If there is some roll-yaw and yaw-roll coupling, and the imbalance is small enough, the side-slip created by the incipient turn will generate enough opposing roll moment to return the plane to a dutch roll instead. But that is an oscillating motion, so you still won't have stable bank angle.