Hi Jim,
I know this is going to sound a little vague, but it will rotate around the vertical axis at the center of mass if it is stationary. Essentially it will rotate around the point where the overall weight of the boat balances. That will be a bit different for each boat due to everyone carrying a slightly different loadout with personal equipment, fuel, water, etc. If you want to get an idea what that point is on your boat, just maneuver to an open area where you can do a few complete 360s, bring the boat to a halt, push the bow thrusters in one direction, and the stern thrusters in the other to get the boat to rotate. You will then be able to see approximately where the point is around which the boat wants to rotate.
Now, to answer a bit more specifically for the bow thrusters, if you are moving either forward or aft, that balance point mentioned earlier will appear to move, as the hull moving through the water adds some stabilizing force. It won't be much though. For example, sometimes in tight spaces I will use the bow thrusters when moving the boat in reverse. The bow thruster will act like a rudder at the bow and will move the bow left or right, with the pivot point a bit closer to the stern than normal. It's really something you need to try and see how it works for you with your loadout though. Hope this helps.
Cheers,
Ralf