I seem to remember this being possible, probably by putting something in init.py or localinit.py, but I can't remember how. Any guidance out there? Thanks.
Golden Goose
I don't remember there being an init setting for that, however you should be able to open the object in nifskope (you will probably have to extract it from art.ff in the "interface elements" directory), and set the flag to hidden. You could alternatively alter the alpha on the texture for the ring to make it invisible as well, but that texture may be used for other game interface elements, so it may have unintended consequences.
I did this a while ago. I found the selection circle as Goggles said, and I set the colors to transparent with nifscope. That made it still there but invisible. Didn't seem to affect anything else in game. I renamed the original file and kept it as a backup just in case there were problems.
There is a line in the init file you can put in order to do this. Unfortunately my computer at crashed today. As soon as I get it up I will get it.
let me know if this doesnt work.
ff.RESULTBUBBLE_SCALE=0.0