We used to put a portable dvd player in bathroom as a distraction. Also you might want to try getting an OT evaluation if you haven't already done it. This sounds like your daughter has some sensory processing issues. The book "The Out of Sync Child" may be helpful as well.

Some calming music that sounds like good advice. My son was the same way he did not want to get his face wet the method I taught him is the method he still uses on his own today at almost 12 years old. During hair washing time I would give him a hand towel to place over his face and tell him to look at the sky or the ceiling and don't look down then I would rinse his hair that way with a cup or shower head so the water would not get on his face that was the part that seem to bother him the most also for you trying to stay calm during her time of anxiety it also might just have become a habit to freak out over bath time

Self injury is always a major concern. You say this method is the routine, are her responses routine as well? Has it always been this way or just recently...ie since school started or other changes. There is a misconception to routines. A "professional" may have suggested it but going into their world over making them follow ours is most important. I would end the routine since it is not going well and try new things. I am assuming she has communication issues because it sounds like alot of frustration happening. Make it a special world in there. Whether its dim lights, soft music, toys, bubbles, bath crayons...etc. keep trying things based on her interests. Paying close attention to triggers happening . Sometimes we ourselves are the triggers when we arent responding how they need in that moment. Been through it all...good luck mama.

thank you guys, I am going to try the music and she really likes art so I think the bath crayons are on the top of my to-do list!

Music or put a flat screen in the bathroom with favorite movies.