is caitlyn in a similar boat as vayne? In regards to caitlyn's passive?
Even if you ignore her other abilities which scale with AD, she'll do more damage with the extra AD, even if she's standing in a bush which would trigger the effect every 4th shot. While that extra shot damage is nice, think of it as icing on the cake - you like it and it's good but that's not the main thing you're after. In most things in this game there's a balance. You have to balance health versus defense for example. If you go all defense and have 600 defense, that's much worse than having like 350 defense and more health items. At about 400 defense, more defense doesn't really help so after that you go health. The same way though, you'll be able to take less damage if you go pure health. It's a bell curve sorta deal.
This same thing applies to AD versus AS. If you go all AS that would be an awful build, pretty much the same if you went all BT. You need a balance to get optimal damage output. The trick is finding that optimal range and when you should get what. For the most part, getting damage early is better for AD carries since that boost in damage will be better than a boost in AS. It's all about the bell curve.
As a side note though, at the same time you might want to go all damage and AS but if you're too squishy, you'll die quickly. If you die quickly, you get less attacks in and do less damage. That's why it's often good to get items such as a Banshee's Veil or a GA on carries, that's another bell curve sort of thing. Too much tanky, you don't do damage, too much offense and you die right away. It's all about finding the balance.
I don't have actual number to show you but I'm sure someone online has graphed it if you want all the details. (Maybe I should make a guide with this info, hahaha)
tl;dr You need to balance it. Early game damage is better than early game AS usually (in my opinion)