Just for the sake of clarity, let's just stick to measuring Voltage, and NOT Current. When measuring the voltage, make sure your meter leads are in the proper place on your meter, and you are on a DC Volts scale of at least 20VDC. Connect your black meter lead to the negative terminal of the battery(or arguably a good ground), and make all of your measurements with the red meter lead. It appears from your posts that the battery voltage (w/o charging lead connected) is about 12.5 VDC. The B+ lead of the regulator(when connected) eventually makes its way to the Positive lead of the battery(perhaps through the Ignition Key Switch).
With the engine running, and your red meter lead on the positive battery terminal(black still on the negative), when you connect the B+ terminal from the regulator, you should see the measured voltage go UP. It will likely exceed 13VDC or perhaps a bit more. If it goes up to a value above about 14.8VDC, your regulator is probably bad. If indeed it goes up, it's a good bet your rectifier/regulator is doing it's job and you're good to go! If you do NOT measure a change, the regulator is likely bad OR there is a wiring problem.
At all times you should be measuring a Positive voltage with the meter leads connected as described. Without having a load of some kind from B+ to ground, trying to measure the output of the regulator while it's disconnected can produce goofy results. Connecting the output to the battery will tell you whether it's working.
Checking the charging circuit by measuring the voltage is, in this case, the best way to test it. I would not recommend trying to measure DC current as this can vary greatly depending on condition of the battery, engine rpm, etc.