I'm having some trouble to find the meaning of this word. I already saw this 2 times in a game and I can't find the meaning in any dictionary that I use.
Examples:
あやせ：「そうなると私のことなんか放っておいて…」
京介： ブチブチと文句を言ってくる…んだけど、あれ？なんだか言葉の切れ味が鈍いような…
and...
加奈子：「イイエ、ナンデモ」
あやせ：加奈子はそのあともブチブチと何か言っていたけど…
From context (such as ブチブチと文句を言って), it looks like ブチブチ has the same meaning as ブツブツ, which is onomatopoeia that corresponds fairly well to grumble, grumble, as when dissatisfied or complaining. See sense five for ブツブツ in the Progressive J-E for examples, or look up ブツブツ in your favorite dictionary.
I also found Google results with ブツブツ and ブチブチ together, which seems to confirm that they're variations on the same thing.
I don't think that ブチブチ is a variation on ブツブツ, but rather a softening of プチプチ. プチプチ is a crackling noise. Softening it to ブチブチ suggests a more annoying, thick type of complaint in this case, which may contain more information/emotion than one would like. A complaint that is プチプチ could be ignored as background noise, but a ブチブチ complaint suggests that the person is laying it on thick and is truly annoying. Of course, describing a complaint with ブチブチ is derogatory in the sense that speech is described as an annoying sound, rather than words.
Buchi is a old showa slang for actions like running away without saying a word, being careless or just not giving a damn fuck? also could be interpreted like sleeping on the switch, when someone sleep in the classroom, ignore a phone call or skive to work.
Buchi is a old showa slang for actions like running away... <- 「ブッチ」のことですか？ zokugo-dict.com/28hu/bucchi.htm