Ok, pulling up LOL replay (forgot I had this), watching an earlier battle with me at 2663 max hp and 77 armor, before I started building armor and after she got BC and LW (I know, oversight on my part), she was hitting me for ~400 damage on her normal abilities and her ult got the last shot for somewhere around 5-600. So, it took her about 4 swings, +1-2 attacks from her teammates.
Also, checking her stats, she had 40% armor pen between LW and Masteries, as well as 20 flat from BC/Masteries/Runes at this point. Meaning at this point she was doing true damage...not surprising given I hadn't built armor yet. My fault...so I say "wow, I'm dumb, I'll build armor!"
I get a chain vest, putting me up over 120 armor, but Riven still hits for over 200 (close to 300) a swing, with the addition of only phage (20 AD, not a big change), and being 2 levels lower than me. Her ult still wrecks for around 500 damage... her combined pen still has her at close to true damage before her ult hits (only 34 of my armor counts).
Ok, I need more armor...right? I'll finish a sunfire cape and grab warden's mail! Super armor HO!
194 Armor now, but Riven's gotten a bit more AD (bilgewater, and finished Frozen mallet)...and now she's hitting for 4-500 a hit? wow! I spent over 3k gold on tank items and she added a little more AD than you'd get from a BF sword (lets say 2k gold worth) and is doing significantly more damage, still...
What is my armor even counting for right now? 194-30% from BC = 136 -40% = 81 -20 = 61
So, for the low low price of around 3k gp, I got less than 30 effective armor...her ult alone is hitting for 5-600 damage even with no BC stacks on me.
Ok, so what if I just went balls to the wall with the Armor? Just stacked Chain vests? I had I think 3 slots left when I started building armor, 3 chainvests would be around 2.1k, for 120 armor (25 more than sunfire/wardens), leaving around 900gp to make 2 of those warden's mails instead of chainvests...ok, that would have put me at 243 armor...or as Riven likes to call it 82. Turning a 140 armor increase into a 48 armor increase...
I guess next time just build HP since they're gonna ignore whatever armor you buy anyway??
TL;DR? There is no way to build effective resists against the amount of penetration available now. Even 1 BC is too many.