If it shorted to ground with a fused line there should be no damage at all. If it shorted to ground in an unfused line then it can do some damage to a battery but usually burns the weakest link first which would be the wire in most cases. I have no idea what kind of a charging system you have since it was converted to 12 volts. If it has a modern alternator with solid state voltage control unit it should be a decent set up for keeping the battery up to spec. If it is an older system with a rectifier and a zener diode then they are only marginally better than the old 6 volt set up.
I would check for any more worn wiring that could cause a short and repair any that are questionable. Also make sure all your terminal and splice connectors are clean for good contact. If your confident that the wiring is in good order, try charging the battery back to spec then keep an eye on it for a while and see what happens.
My old 6 volt 1948 HD 45 solo can only run about an hour after dark (with lights on) then it starts to lose power and the lights get dimmer. The old 3-brush generator just won't keep up very well. I can ride all day long when the lights are off.