Sometimes it's ignorance, sometimes it's prorities. If there's an AP Yi and the other 3 damage dealers on his team (obviously not counting the support for late game dps) are physical, building specifically against the Yi makes you squishier against the rest of his team. This could be extremely bad.

There's also the problem that many of the MR items are highly situational at best. Runic Bulwark should be gotten by someone on your team though, if there's a problematic AP champ. You should have asked your Cho to build one while persuading Sona to stay with the team rather than telling her to stop feeding (which is what I assume happened). The combined auras of bulwark and Sona's W would give your team a big chunk of MR without forcing them to build an incredibly niche item they probably didn't need.

Ez could have bought a warmogs or GA. Lux could have done the same if she was actually getting caught by Yi (which shouldn't be happening). These are more general item choices that would protect them without relying on Banshee bubbles. The problem with Banshee is that it's easily popped by a number of things, so while on paper it counters an alpha strike from Yi, it's more likely to end up blocking a random Olaf axe thrown while swapping pokes.

This can go both ways: she ended up feeding because she went out to ward alone, or, she ended up feeding because no one went with her to ward.

If you see this start to happen, then you should be sticking together (supports should always be the with adc anyways), especially if the enemy team is grouping as well. There's also the possibility that you could turn that around and catch the enemy's support out, or even just a straggler.

Also, with Sona putting herself in harms way like that (frequently from what I understand), it tells me that no one else on the team was warding (though I could be wrong). I suspect that a lot of her deaths could have been avoided if the rest of the team was warding as well, either giving you vision of the enemy so you know it's safe, or just for the simple fact that she wouldn't have had to do it while they were all MIA.

Now that my off topic rant is out of the way, BV wouldn't really have been the most optimal item, for reasons already stated. Sona should have gotten a bulwark, given that she's naturally one of the squishiest on the team, Cho should have gotten an Abyssal because he's going to be in the middle of the enemy CCing everyone, Lux shouldn't be close enough to be hit by his Alpha Strike, and Ez should have been able to get a GA, a Warmogs, or QSS (assuming the enemy had a lot of CC). The suggestion for Athenes on Lux is also a good idea if she wasn't able to position properly.

I find that Runic Bulwark should have been enough to mitigate that Yi's damage. That, combined with just one MR item per other teammate (Cho-Abyssal, Lux-Athene's, Ez-QSS) and he really wouldn't have been much of a factor. Unfortunately, the best candidate to wield the item, as you said, got caught too many times.