My question is, what determines the size of the "bounding box" around an NPC or container? By "bounding box" I mean the empty space surrounding an NPC/container that you can "activate." For example, if you stand in front of an NPC and look at them, you can of course activate them; then if you move your crosshair to the empty space to the left or right of them by a foot or two you will still be able to activate them.

I would like to mod the bounding boxes to be a little smaller than they are because it seems like they get in my way just a little too often for my liking. For example, when I'm trying to pick up items on a desk or beside an NPC, I often accidentally activate the desk or NPC.

I have no idea how to make that mod, so I'm asking you all. What do I need to do?

Containers do not have “Bounding Boxes” they have collision structures in a RootCollisionNode branch.
NPC have “Bounding Boxes” that are stored in animation files (main.nif and x.nif, the most important is x.nif). In order to make that working properly it is necessary to modify “Bounding Boxes” in all animations used by an NPC (hence, including base animations). The later will affect all NPCs in the game (including third person view of PCs). In my NifScope test it is possible to reshape “Bounding Boxes” only to some extend in x, y but not in z (CTD) directions. Bad “Bounding Boxes” could be “corrected” automatically by the game engine.
Because in your case that should be a global replacement I would better stay with the problems you observe than mess up with “Bounding Boxes”. Of cause for your custom containers you can model collisions (RootCollisionNode branchs) as you want.

Thank you very much for the information, A1x2e3l. Indeed, I tend to agree with you that it seems like far more trouble to fix the issue than to just live with it.

Thanks again. :^)