There is a firm logic behind the perfect tune from the banjo bridge. The logic it is that bridge of banjo should be accurately the similar distance from the twelfth fret since is the core. That is why you would not be able to set the position of it by your measurement. The placement should be done to make your instrument play perfectly.
The arena of a string is determines by the length of it as well as by the bunch and stress of it. At the time you set a string on the banjo bridge, its gauge has just determined mass of it. While you need to tune this to a programmed pitch, the tension of it would be a role of the length of the banjo. The theory says that the twelfth fret on your banjo must be center point between the bridge and the nut. Here are some instructions for you for giving a perfect location to your bridge.
You need to lose the strings of the banjo bridge slightly in order that you would not scrape the head of it when you are touching and moving the banjo bridge around. Then you need to use ruler or if you wish you also could use yardstick, then you need to gauge from the core to the center of the twelfth fret. There will be no problem if you don’t have any yardstick, you can easily use a portion of wood and you have to place marking on it at the twelfth fret.
This is the second step for you to place the banjo bridge. Now you have to measure the similar distance from twelfth fret to the head of the banjo and then give a tiny mark of pencil just on the head of the bridge at the distance. Then you need to place the banjo bridge there. Now it is the general location of it.
It is the step 3 for you. In this step, you need to tune your instrument to a standard tuning so that the tune is melodious and harmony. You have to do it carefully by listening attentively or by using an electronic tuner.
In this step, you have to make fine tune for the placement of the banjo bridge. Then you need to play every string unlock, and after that you have to place it in the distance of twelfth fret. By using your own ear, you need to determine that whether the fretted note is lower or higher in the comparison of the open one. If fretted one is higher, then it is because the banjo bridge is so much close to the neckline and the not needs to have a move near the tailpiece. Again, if the fretted note is really lower, then the bridge requires having a moved near the neck. Thing is that if your measurement is correct in the step 2, these movements of the fretted note would be very slight.