Mouthing things, chewing on hands and drooling are normal infant behavior and a healthy way of exploring the world. It does not necessarily represent teething. My toddler is two and still on the bottle. Your problem is it is not about convincing her because you will never be able to do this. The how-to is up to you also.
Some people simply discard the bottle, suffer two or three rough days and then the issue is over.
Finally, I have heard one creative story where a mother and her child carefully wrapped the bottle in a package and a bow for the bottle fairy to take away to another baby who needed it. Whatever works for you is fine. If your child is upset, it will only be for a very short time. Use of a bottle beyond 12-15 months is bad for a child's teeth. So you need to know that you are doing the right thing whether your child agrees with you or not.