How can I teach my 1 year old to brush her teeth without her biting and screaming?

Do your best. Try what you can to make them more interested in it. Sometimes they will chew on it on their own for awhile. There is no harm in that. Most importantly just keep doing it. No matter how much they resist, be the parent and keep after it. They don't understand why you do it, but if you keep after it eventually they will accept it.
Make it fun. Don't let it turn into a battle. Next time you're at the supermarket or drugstore get some different character brushes, and let them choose which one they want to use. My son alternates between a racecar brush and 3 different batman brushes.
Make it fun. Children like to mimic adults. Let them watch you. Don't force them. They will eventually come around and when they do reward them.
Play games. Make it fun and play games. Buy a colorful infant toothbrush and give it to her. Let your child watch you brush your teeth every night and have her copy you. Play imaginary games and be creative with the reasons why you are playing with her teeth. This is a wonderful opportunity to bond. You may have a fight at first but be vigilant and don't give up. Eventually she will ask you to "tickle" her teeth.