The direction of the bias current of LM311
Yes, the LM311's input bias current does flow out of the pins - the schematic on page 3 of the data sheet shows PNP transistors and this implies bias current flows from the pins.
Yes, the LM358 data sheet shows this current as a negative current but, the bias current will be flowing out from the pins just like the LM311.


Some op-amps, notably rail-to-rail input op-amps may specify this as "+/-" because they usually have NPN and PNP combined input stages. But if one of two (or maybe plenty) of data sheets don't obey the convention I don't think it's a big deal - if you have to deal with bias currents (on sensitive applications) you match the input resistances or use low enough resistances around the inputs to minimize the effect. What will remain is the input offset current which can always be presumed to be "+/-" because one input's bias current may be slightly less or more than the other input's bias current.