LM311 Circuit only works when probe is attached
Your scope probe has a mega ohm leakage resistance that is allowing the opamp input bias current flow. It won't flow back into the bridge because the diodes will be reverse biased. 

There's a couple of other problems too such as choice of diodes in the bridge and the potential to destroy the opamp if ac inputs are too high. For instance, you say: -


  Also my input signal is basically a +/- 12ac single cycle burst.


That's a peak voltage of about 16V onto an input pin of a device that is powered at only 5V. Absolute maximum input voltage is +/- 15V. I expect it might be lower than this on a 5V supply.