The general rule for bridge placement is that the 12th fret is EXACTLY half way between the nut and the bridge. Also, you can produce a "harmonic" at the same location, so if the harmonic happens further up (or down) the neck, then the bridge is placed incorrectly.
That said, if the height of the strings at ythe bridge is too high, when you fret them, you will have to stretch the string, and this will put them out of tune. If this is the case, you may need to adjust the height of the bridge, or the angle of the neck.
There have been many threads asking about the technicalities of banjo set-up. Some of these contain links to useful websites (I'm too tired to go searching tonight). Put "banjo" in the Mudcat "search" filter (use the "Threads" one NOT the "Lyrics and Knowledge" search box)and a date limit of 12 months and you should be able to find some previous discussions.
Quack!
Geoff the (banjo playing) Duck.