I ranked close to 1200 after my placements but have had lost 3 games in a row today. My ad carries consists of Ashe, Cait, Corki, and Vayne and I've yet to reach a problem where someone else wanted that role. (and yes I can play different roles, just I prefer carry)

I tend to be passive early game, although I've tried a few times to deny and poke my opponent ad carries. I do make mistakes, I'm not perfect, but I feel as though when laning phase ends, if I'm above in CS and I have maybe an IE + zeal + cloak, and if other lanes have already struggled and may have fell a little behind. Half the times a good team fight breaks out and my team comes out ahead, but if the transition between laning to grouping gets sloppy, the game slowly bleeds out.

tldr:

For ad carries, I feel like my game depends heavily on how well the other lanes hold within the first half of the game. I don't think I can afford to roam unless I have an early tower which is rare, what can I do besides playing another role?

Well, you hit the nail on the head. AD carries are, well, carries. This means they are weak at the start and unless you absolutely crush your lane, you will take a long time to become powerful and able to win teamfights. This means roaming is out of the question, as an AD carry that gets caught early game generally will die.

AD carries are designed to kick in and output high damage late game, but by the nature of being a carry, this means they aren't going to be able to heavily influence the early game. That's the role you are choosing to take unfortunately. There are certain AD carries that are more powerful early game, if you want to dominate and win harass heavily (Urgot is the best example), but these tend to fall off late game and lack the true late game damage output the others have.

You can't have everything, unfortunately. Either you choose a carry that depends on reaching late game to be dominant, which means depending on teammates in early game, or you choose someone who can help control early game better, but doesn't have the same potential.

Mids can carry pretty hard if they win their lane and then gank other lanes. AD carries don't really have that option. Roaming is usually a bad idea because you'll miss out on cs or lose a tower... You really depend on winning team fights for your team.