I don't feel Ahri's ratios are high enough to actually fulfill the assassin role, especially since that all but one of her spells are skill shots. I really expected her ultimate to be ammo-based so you could use it to dart in and out constantly. You can, but it has a 74 second cooldown or so.
Rushing damage items on is the best way to go I think. Doran's stacking into Rabadon's etc. She's great fun to play, just needs some damage fixing.