Really tough spot, BBuddy can be a pretty wild pain in the ass when he wants to be. I'm sure your image is very tight and your 3 betting range pretty thin given the circumstances, it's hard to imagine that the majority of his range isn't AA/KK, maybe a small percentage AK and QQ. I think that a flop push only gets called by AA, you're better off either folding on the flop or calling the flop and folding to a turn shove despite getting good odds on a call.