Merlin said:
No.
Playing bingo is not a sin.
Yes. Playing bingo is a sin.
I'm joking, I actually agree with you, but we need to start providing reasoning.
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Gambling (and thus bingo) isn't a sin by default, but can become one if it causes you to violate the two basics: love God, love your fellow inhabitants of this ol' ball of mud. It is remotely possible (in theory) for bingo to lead to to try superstitious divination or good luck ceremonies, which is denouced in the Bible, assumably for being pointless, at the very least. This does happen more than people taking up any form of magic because of fantasy entertainment, actually, so it's probably not as remote a possibility as I initially thought.
So, is gambling a sin? No. Does it provide you with an opportunity to sin? Yes, but so does Christianity (oh, comeon, heard of the KKK, the crusades, witchtrials, or televangelism?). And we're not about to denounce that.