As Neal mentioned you can check the stator on the bike in isolation from the regulator. You're measuring AC not DC there so set your meter accordingly. At 2000 RPM you should read between 34 and 40 volts between each pair of the three pins on the plug coming out of the stator (a-b, a-c, b-c). The readings should be very consistent also.
The same pairs should Ohm at 0.1 tp 0.3. If greater than 1 Ohm the stator is open. Checking from each of the three pins to ground should show no continuity.
The behavior you describe is very likely going to be a regulator (unless you find a loose battery cable connection somewhere -- check each end). But it's not a big deal to check the stator by itself so you know for sure before buying one or the other.