While I'm *far* too lazy to pull any books off my shelves or consult past writings to check, I'd have to go with the following:
If it is an object or activity, A/B (e.g., "I'm bored with this Rubik's cube."; "I'm bored by football.").
I would tend to use C more activity-exclusive ("I'm bored of this game.").
That's what seems right to my eyes & ears, and that's how I would use them.
Frankly...I am seldom if ever truly bored, so don't often say it ;)
@stueytheround
If anyone can provide language rule/precedent, I'd be keen to know; I am not aware of it from any canonical works (e.g., MLA, Strunk & White, LB, etc).
That said, I'm widely due for another reread of S&W. My overutilization of needless words is not just awful: it's *gawd* awful ;)
(Yes, that was deliberate) :D