Excellent explanation! (For us who love the science behind it all)
So since everyone's bridge hand is a different length from the cue ball and their back hand is a different length from the butt of the cue, along with, both hands are a different distance between each other, oops, also forgot about cue tip size. You would need to calculate your own size of the "Bulls eye" circle. (I know, everyone is thinking, Impossible!)
Not really, Nate said if your bridge hand is at the 1/3 length of your cue spot (measure your cue and divide by 0.3333333), and 1/8 inch (0.125) movement of the tip from that pivot point is a score of 5, that means 1/4 inch (0.25) movement is a score of 0, or outside the circle. As a comparison, take a 1/4-20 nut, look at the hole in the middle, that hole is 1/4 inch in diameter.
However not everybody holds their hand 1/3 of the way from the tip. You will have to find your own "dilution of precision" (because I can't think of a better phrase right now).
Since Nate have given us rough estimates based off the formula, you could find the 1/3 length of your cue and place your bridge hand there (the pivot point) and with the tip at the cue ball move the tip up and down and side to side 1/4 of an inch noting how far the butt moves (find a good way to measure it accurately) then move your bridge hand to your normal spot and move the butt the same amount to see if it is more or less than the 1/4 inch diameter circle. Now you know how big your Bull's Eye is.