I don't agree with you, Freshwalrus. No mastery set is bad, ever. Masteries are where a player builds his own style, this is where your style is coming from. The items will be roughly the same at every Irelia (depending on if they go AP or AD/AS). I can see why she's using so much utility. Irelia has mana problems if you use her skills a lot. I, for one, want to be able to maximize that bloodsurge and Hiten Style all the time. What do you want? CDR. Not with items, I want it just like that. With 9/0/21 you have a good CDR from the start up, and with golem you'll be perfectly fine. That's where you only have to focus on AD, AS and Lifesteal. I also use these masteries (although, with some small differences).

shes not a mage, bad masteries, shes a meleee dps, ur not capitalizing on rune potential, build hybrid on her works theoretically cause her ult scales very nicely with ap, but ur ult is one attack, u limit urself by not building pure ad/as. you can basically build her like xin zhao, life steal, crit chance, attack speed(as) and ad.

I totally Agree with Dalek Jace.. I always start off with Vapiric Scepter. Just gives me more laning time early on i.e more gold/exp for bloodthirster.

Her ultimate takes either AD or AP, not both. I'd get rid of the AP items if I were you. The Ultimate scales with 60% of your AD, and with 40% AP. Unless you go full AP (which I wouldn't recommend) AD will be a much better choice.
I also prefer to start with a Vampiric Scepter and Boots (Upgrade to whichever helps you the most, I prefer Berserker's Greaves). After that go for B. F. Sword > Bloodthirster right away.

Everyone his style though, attack speed is real good with Hiten Style.