Hiya! I came up with this build due to AP Zeri getting nerfed again in this coming patch. I really enjoy AP Zeri's gameplay, so i tried to make a AD build that continues to put power into her W.
This build is identical to AP Zeri at the beginning, but it tends to fall off a bit after you get Manamune until you can get Immortal Shieldbow and Infinity Edge.
Once you hit three items and beyond, you do a ton of damage with your W and Q alike, however the burst damage on your R is decreased compared to AP Zeri, but you make up for it with the ability to spam your Q better.

Try to make as much use of First Strike early on, espeically against melee laners. remember that Zeri's right clicks have an execute on them, so use that to help CS. Once you hit level 2, look for W's whenever your lane opponent goes to CS. After you purchase Tear of the Goddess, you don't have to worry about missing, so use your W off cooldown for harrass and clear! If you lose lane, be sure to play safe and try to scale, you need to hit Infinity Edge.

Once you hit level 6, you can go for Max W Zeri's best combo, which is W-E-R-AA-Q. This is a very bursty combo, and while it is better when building AP Zeri, AD Zeri can follow up better after the R, with more Q's. After getting boots, look for chances to roam to herald or dragon to try and turn the tides in your favor with some good W's.

AFter getting Infinity Edge, the burst combo I mentioned earlier becomes much stronger, so look for fights more often. Always try to follow up CC from your teammates with a W. try to focus squishier champs to pick them off. When you get your full build, you can fight with your whole kit very well, so dont be scared, but think before you act.