Well, first of all, Statikk Shiv has never really been a viable start on any AD Carry. I've seen it a few times on Tristana and maybe Vayne, but that's generally if you're very behind and need the gold from the early avarice as well as the waveclear Statikk Shiv provides. Twitch doesn't exactly have an oppressive laning phase, but he's far from having the worst, so unless you're playing poorly, you shouldn't be too behind in lane. Additionally, W, and auto here and there, and then E is decent waveclear for twitch.
I can give you a few reasons as to why Bork is an effective rush on him. First of all, the attack speed just synergizes excellently with him. You generally won't have an optimal item, especially Infinity Edge, completed before level 6. Twitch also, scales incredibly well with attack speed, being able to apply many stacks of his passive, and also being able to get more attacks in while his ult is activated, thus effectively, hitting more enemies. Add this onto the fact that the more stacks he gets, the more amplified his E becomes, and attack speed just seems to make sense. Twitch is far from a caster ADC, focusing more on his auto attacks to do damage than anything else, so the percent health damage on each auto attack in addition to the true damage from his passive, makes shredding tanks a breeze. (Plus, a little life steal in early skirmishes never hurt anyone except the enemy). To add on to the tank shredding capabilities, a second item, Youmuu's Ghostblade is also effective. Early on, when it's a bit more difficult to secure CS, an avarice blade is effective for making every Creep kill count, increasing your gold income. In addition, the Brutalizer's armor penetration helps also in fighting tanks. After that, Infinity Edge, Bloodthirster or PD, and a Mercurial Scimitar should be good to round out your build.