Hmmm...well, if it were ME, I'd say...
"Well, what happened this morning can't happen again. What do we need to do to prevent it?"
And if I didn't get anything constructive back, I'd say...
"Okay, we know that you struggle with transitions (list examples). Everybody has something that is hard for them, and this is hard for you. So, we need to do some things to help you figure out how to deal with this." Maybe give an example here of something that is hard for you, and what you do to compensate. For me, I must have things in order or I feel very scattered and unprepared. A long time ago I learned to make lists to keep everything organized, and to prep my things the night before so I could be confident they were how they needed to be.
So, maybe the way for her to cope is that there is an exact list of things that must be done the night before, including a point about anything unexpected, like a note from the teacher or something.
Then, another exact list of things in the morning, including decisions about what to wear the next day, how to do hair, etc.
Explain that you want to help her develop good habits for when she is a grown-up, and this is what you have to do for a while to ease her through this hard time. After a while, start to relax just a little. Maybe suggest she'd like to do her hair differently one morning than she selected the night before.
Maybe also start using a timer to cue her in on how long she has.
It also sounds like performing under pressure is difficult for her, so think of ways to teach her HOW to diffuse the pressure, or avoid it all together, if possible. (Changing your hair style 5 minutes before the bus comes doesn't go well for you. So, let me do it, or leave it how it is. You can't handle that stress yet.)
Be gentle. Respect her, and approach her from a place of "this seems to me to be your needs". You want her to get in the habit of evaluating where she is on the "who I want to be" track, and help her get there. Just this morning, I was discussing with my 4yo about how she had acted like the picture studio was playground. Was that how she wanted to people there to remember her? That she didn't know how to respect public property? What could she do differently to leave the impression she'd like to give?
And no. I don't think it's normal. I think she needs some boundaries and some practice controlling herself.
"If you keep doing the same things you've always done, you'll keep getting the same results you've always gotten."