The correct spelling for the phrase "become bore" is actually "become bored." Bored is spelled with the long "o" sound and the "ed" ending. In phonetic transcription, it would be written as /bɔrd/. This common misspelling might occur because people mistakenly assume that the past tense of "bore" is "bored," but it is actually "bore" as well. It's important to remember the correct spelling to avoid any confusion or misunderstandings in written communication.
The phrase "become bore" does not have a distinct etymology. It seems to be a combination of the word "become", meaning to begin to be, and the word "bore", meaning someone or something that is dull or tedious. The phrase "become bore" itself is not commonly used or recognized as a fixed phrase in the English language.