What is the etymology of the word バレる, and why is it often written with katakana?
ばれる(P); バレる (v1,vi) to leak out (a secret); to be exposed (a lie, improper behaviour, etc.) (behavior)
その秘密はついにばれた。 The secret came to light at last.
The verb bare-ru is a 下一段 verb, so you can expect that it was 下二段 bar-u before that, hence bar-u > bar-uru > bare-ru. It is noteworthy in that it begins with a voiced consonant (b), which essentially does not happen in words of Japanese origin. Rather, it is more likely that it is a recent contraction of another word, which I assume was abare-ru (暴れる). And in fact, it is a recent verb with early citations from the mid 17th century. Reasons to write it in katakana are 1) lack of kanji, 2) emphasis, 3) colloquial. Hiragana works just as well, though.
The accepted answer to this question on chiebukuro suggests that there is no sure answer to the origin of バレる. Some of the suggestions given include 暴く/暴かれる, 破{ば}れる, and 晴れ晴れ.