The build is pretty nice, but getting your boots(lvl 1) before BF sword will help you a lot in harass and last hits and helps you to escape better.
Personally i get IE befor BC, IE gives you more attack dmg, with your zerker boots, you have decent AS and IE gives you a lot higher chance crit and it makes you deal more dmg with crits, the stacking armor debuff looks very nice, but most ppl won't have defensive items yet so you'll hack trough them even without armor debuff, IE fits better in that part of the game, when ppl get their defensive items, BC is perfect.
For the last bloodthirster I rather get a PD, you damage is high enough and when you get that far in the game to get 2nd bloodthirster, your enemies will have quite some armor, so i rather attack faster, crit more and get in and out easier than some dmg increase and some lifesteal, and as you said in the cons, she lacks a bit late game, so a more defensive item like PD is better than a BT, where you have to be offensive for to stack it up.

For masteries, I would pick up Lethality and drop the butcher and vampirism, your build gives you enough lifesteal and dmg to minions isn't important, with some AD your boomerang slices trough them without probs.
I would also drop Greed and take Runic Affinity, when you can get red or blue, you will do insane dmg, 20% more time on those buffs, lets you own even harder. The 0.5g isn't worth it.

For runes, ArP marks have more effect than dmg marks. Quints, get another str or arp quint instead of MS, your boots give MS and when needed, you can use your ult for it, the cd is pretty low, so it doesn't matter when you have to use it defensively sometimes. Armor seals are great, you're squishy. Maybe get MR glyphs, later in the game you won't have that much mana issues and for early game you can bring some mana pots. CDR glyphs could also suffice, however sivir already has low cd's and more defense would be better, since you don't build any defensive items in your main build.