While he did not answer your specific question, you'd do better to get clarification from Ken rather than insult him, he's very active in the game and on the forums and knows his stuff.
To answer your question: No. Building BV against that team would have done little to nothing to slow down that AP Yi. It would be a lot of gold dropped primarily for a shield that would get taken away very, very quickly by an Olaf axe or Taric. Hell, knowing what you were doing, Hec could have just as easily initiated every fight with his ult and popped all the bubbles. And there's no way Sona would be able to afford one, and she was behind in levels and gear, meaning that worst case scenario is that Yi kills her and pops all the bubbles with Alpha, then just presses the Alpha button again.
I get what you were trying to do, it wasn't the worst idea, just impractical. The only tools you had to lock down and kill a rampaging AP Yi were Cho Q or E (which you said he missed plenty of) and Sona ult (which is a considerable cooldown and would put her in harm's way to get blown up anyway). Once Yi started getting out of control, you had very few tools to deal with him. Pretty much you would just want to keep stacking damage on Ez and Lux, hope they position well, catch Yi outta position with a Rupture and jump his ass quick, locking him down before he can Alpha or Meditate. You woulda had to rely heavily on Cho to do well to pop and silence him, and since he apparently couldn't, you were boned from the time Yi got fed.