Can't imagine the battery having 60 volts unless there is a serious lack of electrolyte inside, or an outright open circuit within.
However, if it does, your fuses will probably go poof in a big way.
At 12V the bike normally draws about 10 amps. This equates to a bike circuit resistance of about 1.2 ohms. The bike resistance isn't going to change (at least at first application) even when 60V is put on it. However, the initial current draw will be 50 Amps! Your main fuse ought to make quite a lights show, being it is supposed to open at 15-16 Amps. Good thing, too. 60 volts make your 50 W headlight into a 1000 watt device... for a few milliseconds anyway.
The charging system is direct connected to the battery with no fuse.
Check your charging system rectifier and use a known good battery for further checkout.
And get a new main fuse.

Cheers,