Both are certainly possible, and bored by
comes more naturally to me. Looking at the examples rom the Cobuild concordancer
I wonder if bored with
is only used with concrete things, whereas both bored by
and bored with
are possible for both concrete and abstract ideas. But use the site to have a look at more examples to see if this holds up. Bored by
... Well, ask me something he says, politely bored by the virtual-reality computer game smashing
... Indeed, many looked bored by the speeches and were impatient for the ..
latter is a military megalomaniac who is soon bored by the innocent toys the company produces,
...were shocked by the programme's ambition and bored by its technicalities.
In prison he had not been bored by solitude, but had often been irked by ... Bored with
I'm bored with my bedroom. Over the past years it's
looked like this since I was a teenager and I'm bored with it
... at the age of 27, bored with my job as a small-change magazine
And I must admit, I was getting rather bored with lying on the sofa all day, eating ...
...an interesting man, `It was impossible to be bored with him!
she had known him he had challenged and become bored with skin-diving, mountain climbing ...
after sixteen years of marriage they have grown bored with each other. They may have fallen out of
... you'll probably be bored with life, and people will be bored with you.
...a dry man-of-the-world cynicism, as bored with left- wing enthusiasms as with religious ...