photodiode current direction
You can connect the photodiode in either direction (anode to GND or cathode to GND). Both variants work; the difference between both variants is just the polarity of the signal.

(You need to look up in the datasheet of whatever diode type you are actually using to find out which of the leads is the anode/cathode; or just measure direction of conductivity of the dark diode).

The current direction in the photodiode will be opposite to the "arrow" direction of the diode circuit symbol, i.e. inside the diode from cathode to anode; outside the diode from anode to cathode (as indicated by the \$I_P\$ arrow in your circuit diagram).

BTW: there is no reverse bias voltage as both OpAmp inputs will have about the same potential, i.e. the voltage across the diode will always be very close to 0V. The Output voltage of the OpAmp will create a current through \$R_f\$ that will exactly compensate the photo-current created by the diode. 

The diode works in photovoltaic mode.