What bias voltage is applied to a PIN photodiode when connected only to multimeter
expose the photodiode to the sunlight and read current of ~1 mA on the multimeter.


I will assume this means you're using the multimeter in ammeter mode.


  In what region do I operate the photodiode with respect to bias voltage, that is do I have zero, forward or reverse bias voltage ?


The meter should not be applying any bias in ammeter mode.

It will have a small "burden resistance", meaning as the photodiode starts top push current through the meter, the voltage across the meter will increase slightly.

The result is you are essentially using the photodiode in photovoltaic mode, but with a very low load resistance (which isn't how we typically use photovoltaic mode). 


  What is the bias voltage (or how it can be found) if not zero ?


You could put a second meter across the photodiode and put it in voltmeter mode.