At 2yo I'd honestly cut the bottle out. if he's shouting for his bottle then it's habit based on his digestion. He really doesn't need a feed that early at 2yo.
I'd get him up & distract him & not offer him the bottle anymore & hold out on food for as long as possible. I found with my DS1 (he was only 1 at the time) we got some improvement - closer to 6, by not offering any food until 7am... he was still an early riser, but it wasn't as early... sadly my DS2 was an early riser, but as he didn't ever get milk or food until 7am (unless he hadn't eaten since 2 or 3 am) I couldn't even blame an early feed on his early waking.