We found one dictionary that defines the word bored out of one's brains:

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1. bored out of one's brains: Wiktionary

Definitions from Wiktionary (bored out of one's brains) ▸ adjective:  (informal) Extremely bored. ▸ Words similar to bored out of one's brains ▸ Usage examples for bored out of one's brains ▸ Idioms related to bored out of one's brains ▸ Wikipedia articles (New!) ▸ Popular nouns described by bored out of one's brains ▸ Words that often appear near bored out of one's brains ▸ Rhymes of bored out of one's brains ▸ Invented words related to bored out of one's brains