it's easier to get rid of the bottle if you get rid of the binky first. My kids were all different.
1st baby off binky at 3 months (mainly because it was recalled and he wouldn't take anything else but after a few days he was over it) off the bottle when the dr told me at his appointment at 14 mths.. new mom had no clue they wanted them off the bottle at 12 mths. bottle was gone that night after his appt. fussed off and on first night without the bottle then he was over it.
2nd baby had colic for 5 1/2 months. She had her binky until 9 months--fussed a few nights.. was off the bottle at 12 months.
3rd baby weaned himself off the binky at 5 months and he kept throwing his bottle across the room at 10 months and several of them cracked (they were plastic) so I told him if he threw one more bottle that was the last one so he weaned himself off the bottle at 10 months when he threw another one and never fussed for it.
Once you decide to take it away stick to that decision because once you give it back it is much harder to get rid of it...plus you are sending a message that if they whine or fuss enough they will always get their way. I didn't have whiny kids, they knew when I said no it meant no and even now as teenagers they don't argue with NO. A lot of babies will fuss for a few nights missing the binky or bottle but they will realize that it's gone and you won't have to deal with them being totally addicted to it as a 2 year old and a hard habit to break.
I feel that once your baby no longer needs the suckling sensation that newborns need then is time to get rid of the binky before it becomes a habit and most babies grow out of that need by 6 months. If they don't suck on their fist a lot they are growing out of that stage.
You will get several opinions as to how long to keep the binky or bottle but letting you know my experience with 3 kids and none of them were attached to a blankie, stuffed animal or anything else. They learned to become independent and entertained themselves at a young age. now as pre-teen and teenagers they can do every chore, cook just about everything we can cook, and are hard workers, very involved at church youth group, and like to read and play games so they are rarely bored.