When you measure AC, you get an RMS (Root mean square) value, but since this is AC, the actual voltage varies from -Vrms*sqrt(2) to +Vrms*sqrt(2) (in case of pure sine wave). So, for 9V this is -12.7V to +12.7V.
If you rectify this with bridge rectifier, the negative half of the wave gets flipped pver and you get a wave with voltage from 0 to +11.5V (I figured 1.2V diode loss)
When you put a capacitor accross, it gets charged at the peak to 11.5V and, if there's no load it stays that way, so you should measure 11.5V on the capacitor.
When you add a load, the capacitor gets discharged between peaks, may be severely, depends on the load and the capacitor, so the average voltage you measure will be less and less.
At the same time, as others said, when you increase the load the voltage produced by the transformer decreases. That's why you get 13.5V instead of expected 11.5V without load, but it goes down when you apply the load.
Therefore, both capacitor and transformers may be suspect,
If you cannot get 55mA from the transformer rated for 200mA I would suspect the capacitor first.