When we're reasoning about chemical reactions and their mechanisms (in organic chemistry in particular), the way we model the behaviour of molecules is almost in a “common sense” way.
When the reasoning happens in our heads and on paper, it is easier to use heuristics than quantum mechanics. The chemical reactions are governed by quantum mechanics, of course, but you can predict quite a bit through analogies to known reactions in your head without doing a quantum chemical calculation.
This works particularly well in organic chemistry because many reactions involved functional groups of a limited set of atoms (C, H, O, N, ...). Of course, organic chemists use almost the entire periodic table when it comes to reagents, but those are a given for a type of reaction, and you ask whether you can apply them to a new organic molecule, having tried them for a lot of cases already.
Is this because reactions occur in the bulk, and even though we are thinking about what is happening in terms of the behavior of individual molecules, that molecule actually represents some sort of average behavior of the bulk, and so quantum effects/weirdness are being averaged out and we can think of them acting in a more “common sense” way?
No, each single molecule has to react independently, so it does not help that the molecules are present in bulk (like it does for equilibrium thermodynamics). In fact, the "cheaper" computational methods such as molecular dynamics are not so helpful when trying to predict chemical reactions.
Of course I understand that the actual bonding and our understanding of chemical structures and things like that comes from QM based models.
Traditionally, QM was used to study very simple systems (dihydrogen reacting with proton, for example), and you had to extrapolate to more complicated systems. This is changing as methods and hardware become more powerful. Once you have a handheld device that can do a full QM calculation on the reaction you are attempting in the lab, I'm sure chemists in the lab will do a quick QM calculation before starting the wet chemistry, but we are not quite there yet.