You may be asking "What the hell this guy intends with AD Katarina?". Well, I like to try new builds and I decided to give this one a chance. And, yeah, it works. Besides the damage with Bouncing Blades and Death Lotus, her auto-attacks become very strong as well. In mid game you can easily go jungle because with the lifesteal from Bloodthirster you practically lose no hp.
Maybe Shunpo won't be very effective when it comes to damage, but, on the other hand, your auto-attacks can compensate this lack of damage.
So, before criticizing, try it and see what happens.

I think there is no mistery about Summoner Spells.

Exhaust allows you to counter that DPS and he won't be able to escape from Death Lotus.

Flash can be used in different occasions. Either running to save your life or chasing a enemy along with Shunpo.

Ignite is a nice alternative instead of Exhaust. It helps with that little bit of life missing to get the kill.

The rest of the Summoner Spells can be used according to your strategy, but I think the ones above work better.

Starting with Boots helps you escape or run after enemies.

Then turn it to Sorcerer's Shoes, which helps very well with that magic penetration.

The Brutalizer is very effective because of its Cooldown Reduction and Armor penetration, besides the damage.

After that get B. F. Sword and Vampiric Scepter. Once you complete your Bloodthirster, start stacking and care not to lose your stacks.

* OR *

If you feel you can get a lot of kills, grab a Sword of the Occult, but beware because that will call the enemy's attention to your head. Well, they focus you anyway since you are Katarina, so whatever.

At this time of the game, it's interesting to get a Guardian Angel because the enemies will be focusing you very hard, unless they are brainless.

After that, get your last 2 Bloodthirster and your damage will be just great.

But there's a nice alternative. Zhonya's Hourglass can be really useful in teamfights. Just after using your ult (or before it, if necessary) active this item and enjoy 2 seconds of peace. Besides that, its Armor and Ability Power are very good.

That's what I got from this build. Hope you get the same :D