Well, there's a lot more going on than I can account for. And I really shouldn't be surprised.
I tested a bolt:
mass = 11.1 g
length = 30 mm
head diam = 12 mm
thread diam = 8 mm
thread lead = 1 mm
This bolt was designed to fit:
flanged metal nut 3 (numbered for previous experiment)
mass 6.9 g
thickness = 8 mm
outer diam = 18 mm
inner diam = 6 mm
As the reader will have observed, there are notable differences between the screw in the first experiment and the bolt in the second. These differences may account for the opposing observed differences in results. Or they may not. In my opinion, only further experiments will decide.
Apparently there in no strict definition that distinguishes a bolt from a screw. For myself, I've always thought of a screw as 'the mechanical pin that can be turned and tightened into place as a result of its thread with a screwdriver' and a bolt as 'the mechanical pin that can be turned and tightened into place as a result of its thread with a spanner or its analogue'. It's a personal, tacit definition, and I'll stick to it for the purposes of this exercise.
The bolt and nut are not a 'tight' fit which I would consider to be something like a screw in wood; but rather an 'close' fit. That is, the bolt and nut were machined for each other.
In this experiment, the nut was clamped between the two pieces of wood which in turn, was clamped in the vice. Also, the nut was clamped so that bolt was vertical. That is, clockwise rotation resulted in the bolt going down with gravity. Note that the head of the bolt is not the end of the bolt upon which the drill bit is acting on. It is hexagonal and so it is not possible to apply the drill bit and have the bolt rotate freely. No lubricant was used.
Perpendicular drill bit orientation resulted in bolt rotation but in a random way, with no overall discernible pattern.
Parallel drill bit orientation predominantly resulted in bolt rotation in the opposite direction. This is as one would expect: the drill bit was engaging the bolt as though it were a cog but not matching rotational speed like a true cog. However, the bolt would occasionally stop, and occasionally momentarily turn in the opposite direction.
Simply stopping I could explain by simply assuming that the bolt and nut frictional force at that time was greater than the resultant torque from the friction between the drill bit and bolt. But to turn the other way, even momentarily, means there is more than just a simple balance between frictional forces with a net result in torque.
I should add that I could not control these same direction of rotation events (SDORE). They were fleeting when the drill was rotating clockwise (so the bolt was going down with gravity) and were fleeting anticlockwise (so the bolt was going against gravity).
I tried different orientations and points of contact on the bolt. Some resulted in SDORE more frequently than others. Some resulted in no SDORE that I could see.
I could try a few more follow up experiments, but I strongly suspect I don't have the equipment, skill or knowledge to figure out what's really going on here.