Discussion Forum—A Way with Words, a fun radio show and podcast about language

My guess is that bored of is influenced by tired of. I wouldn't correct folks, but it is pretty easy to avoid in your own language.

You omit the option of bored by, which I think is a good substitute for bored of. For me bored of and bored by convey a slight nuance of the more passive victim, whereas bored with seems more active. This is not a strict division, but a personal observation.

I would tend to choose bored with for an activity in which I am engaged, or in which I once was interested, but no longer:
I am bored with this book.
I am bored with this game.
I am bored with this tea.

I would tend to choose bored by for a situation to which I am subjected, or which I never held interest in:
I am bored by his complaining.
I am bored by this painting.
I am bored by this TV show.

Again, describing my choices, if I were to say:
"I am bored with country music" I would most likely mean that I used to enjoy it, but no longer.
"I am bored by country music" I would most likely mean that I simply don't find it enjoyable, and probably never did.