What you need to do is to separate the issue of falling asleep from feeding. There are a couple of ways that you can do this. In general you should go ahead and give a baby this age a bottle before she goes to sleep, and you can combine this with some quiet activity such as looking at a little picture book while the baby is on your lap. Once the baby has finished the bottle she should be somewhat drowsy, though still awake, and at that point you can pick her up and put her in the crib awake, and allow her to fall asleep on her own. This can be difficult and often babies will start to cry. However, if you use some reassurance, pat her a little bit, or hum a quiet song, usually within a few days you can get her to learn how to fall asleep without sucking on the bottle. There are a couple of good books available that discuss sleep in children and how to manage sleep problems. You can find them at most bookstores.
Find out how to break your child of the need for a bottle to get her to fall asleep.
I feel really guilty about this but I have a problem with my eight-month-old going to sleep. Whether it is a nap or bedtime, she almost always has to fall asleep with a bottle. Sometimes she won't accept it and I just hold her and let her cry and fight until she falls asleep. How can I get her to fall asleep on her own? It is so obvious when she is tired, so why won't she go to sleep? I am afraid that falling asleep with the bottle will rot her teeth. She already has two bottom teeth.
There are actually two issues that you bring up in your questions. One issue is how do you get a child to fall asleep on her own, and the other issue is what the effect of having a bottle on the teeth is. You are absolutely right to be concerned about having frequent contact with the bottle. Children who sleep with the bottle, meaning that they have the bottle with them in bed all night and are sucking on it frequently during the night, are well known to have significant risks for developing severe tooth decay. This is because of the carbohydrate (the sugar) that is in the milk or juice in the bottle. The milk ends up "bathing" the teeth all night, and it can cause tooth decay just as candy does. Just falling asleep while sucking a bottle is actually a different issue, however. Presuming that the child does not then have the bottle in bed all night, there is not a concern about rotting the teeth. The issue is that the child has only learned how to fall asleep while she is sucking, so that if she is not sucking she can not fall asleep.