The rectifier bridge is doing something strange, that's for sure. Bridge output to the meter is a 100 Hz sine wave shifted up to be all positive.
This then makes sense that the meter only shows about half, but I still don't get the bridge behavior..
Increasing the capacitance across the meter/bridge to 10 uF gives some DC component, but not much..
The RMS voltage across the meter is close to 100 mV, which would translate into 0.5 mA through the meter, which would give the expected reading, so the current transformer and meter are working as expected.