I've recently been playing Caitlyn solo mid (I was playing her bot but found that she was more suited to 1v1) and I found that she is well suited to pushing against champions that, using abilities, can't penetrate through minions. In this situation, however, it's best NOT to get as much damage as possible with your peacemaker by moving out from behind your minions to find a more desirable angle but to actually shoot from behind your minions (whether his minions are in the way or not (if not then bonus!!)). This is because those abilities that don't penetrate usually do more damage or cooldown faster than your peacemaker. You also have to strategically place traps to keep him in front of your minions.
It's a shame that the net takes so long to cool down at level 1, this is a great tool for escaping those ganks when you cross the river or even no crossing the river. It's a shame how it doesn't affect Master Yi when he's using his ultimate.
Headshot and Peacemaker are, in the laning phase, your main harassment tool. I use headshot on the enemy whenever it's available (I try to stay just in-range of him so that I can use it on them whenever it's available). The Piltover Peacemaker I use, usually if there is no minions in between my target and I but if there is only 1 and their shots don't penetrate then I use it. I don't tend to spam it (unless they are killing my minions faster than I am killing theirs and I need to push him out of the lane).