Bored with is the usual collocation in common-core English, but bored of is an option (Peters 2004, 76) of which CIC British texts have 3.1 iptmw and American texts 0.7.See also, bored of, Language Log: Bored of, and
Source: British or American English: A Handbook of Word and Grammar Patterns.
General Writing and Grammar Help: "bored of" or "bored with", teenage son, question mark
The usual preposition to use after the adjective bored is with, as in I got bored with all their squabbling. However, nowadays you increasingly hear — and see — the preposition of being used, especially in informal contexts. (One possible reason for this is the influence of tired of, which has a similar meaning to bored with.) However it’s still best not to use‘bored of ’ in careful speech or writing.
Source: Good Housekeeping :: Spelling and grammar