I'd move caitlyn up the bot tier list.
-against gap closers, its often ok to take the first hit (like a jax jump) then just E away and trade damage back. A clever trap can give you a couple more hits too
-With her range, Lightbringer is a fantastic item. If you're defending your bot point against a push and see them running down to get the health relic. Shoot them once as they run past, then continue to shoot over the wall with vision.
-Her Q is great for pushing and harass
-I run Revive so if I die and they rush my point, I can revive and ult right away to stop the capture.