Estimated impedance of a 12V bleeper?
The test with the capacitor will give you some idea, but measuring the current outright is a much better way.  The problem with the cap method is that you don't know what voltage it discharged to, and the time is also a function of the beeper current at less than intended voltage.

However, let's see what it does tell us.  220 &micro;F at 15 V is 25 mJ.  Let's say the beeper quit at half its rated voltage, which means 3/4 of the energy of the capacitor ran the beeper for 3 seconds.  That's 18 mJ / 3 s = 6 mW average power usage.  The peak was probably substantially more than that.  We have no way to know, which is why this method is not optimum.  Let's say that at 12 V the beeper uses 60 mW.  That would be only 5 mA.

Again, to get a real answer, measure the current directly.  Perhaps the ammeter is not giving you a good reading because the beeper is switching on and off rapidly.  Put the 220 uF cap accross the ammeter when measuring the current.  That will smooth out the apparent current somewhat, perhaps enough to get a stable reading.  Or, use a old fashioned analog ammeter.  The meter movement will smooth out the current nicely.