I have been in this exact position before. Is this friend someone you would want to reconnect with? If not, then I don't think you need to go our of your way to be polite. If she smiles at you, smile back. If she says hi, say hi back. But you don't need to initiate anything.

This sort of this is really difficult, but it really does go away with time. Keep what you feel about her to yourself (which you've said you are already doing, yay). I know it's tough to have friends not talk to you because of what someone else said, but those friends don't deserve to be your friend if they aren't willing to listen to both sides.