It has been a long time since I had to use a Wheatstone bridge. I think the highest resistance in it was about 1 megohm. The galvanometer does not carry any current when the bridgre is balanced, but the high-meg resistor R would have to carry ~1 volt/R amps, and the galvanometer might have a full scale deflection of ? 1 microamp ?. So the galvanometer should be replaced with a low-offset op amp. For 10^8 ohms or higher I would either build a low input bias current/low voltage offset inverting transimpedance amplifier, or buy an instrument from Keithley Instruments.
Bob S