Ezreal's main source of damage in the early game is his Q, which isn't affected by crit or attack speed, but does apply on-hit effects. This means that going the usually infinity+PD build that you go on most AD carries is inefficient on Ezreal. Also, as AD you want to make full use of Ezreal's passive, which means you'll be spamming your abilities a lot, making Triforce + Bloodthirster a much better option for him.
I've actually done quite a bit of theorycrafting when it comes to Ezreal, to find his most optimal build. I compared the damage out-puts of Sheen + Dorans blade vs a BF sword and unless you manage to get at least 2.0 attack speed, Sheen gives a much higher damage output than a BF sword. Because of this, the build I would use is the following:
Boots + pots
1-2 Doran's Blades
Sheen + Vamp scepter
Attack speed boots