First of all tell your daughter this is not about her, it is about the mean girl..
I know it hurts her feelings, but she is not the one with the problem.. The other girl is the person that is insecure.
Purchase the book, "Queen Bees and Wanna Bees". Read it together.. It will explain it all..
The best way to put someone in their place is through indifference. If your daughter can totally ignore this girl and show that each time this girl is still paying attention to your daughter, others are also going to notice it is a one sided problem.
You know the drill, tell your daughter to just stay out of the way of the bully and her friends. Try to find other people.. does not just have to be girls, that seem interesting.. She can eat with them, walk to class with them, find out if they are attending activities.
Find some school activities your daughter is interested in and have your daughter join. Have her volunteer for upcoming school events.
If the library allows students to volunteer in the mornings, or at lunch see if your daughter would enjoy that..
At our daughters middle school, there is a lunch bunch that plays chess, another that puts together jigsaw puzzles.
The school paper and yearbook always needs volunteers for photography, interviews and artwork.
For school fairs and dances, they are always looking for students to volunteer to put up signs, sell tickets and snacks and decorate.. See if there is anything like that available..
Sports are an awesome way to be part of a community and 6th grade is still young enough to learn and participate in school sports..
I also suggest that your daughter go and speak with her "lead teacher, Advisor or grade level counselor.. just to give them a heads up.. about what is going on..