Hi CM, I am taking a good guess from what you're saying...it sounds like she may have either read a book, or seen a video, or talked to a classmate, and learned about another mommy who either got very sick or passed away, something traumatic. It can really make a child cling tightly to the parent. She might be afraid it will happen to you, the poor little thing! Because you also mentioned it happens at bedtime routine, I think her fear is when SHE CAN'T SEE YOU and be sure you're ok.
Does the teacher have mystery reader day, when you can come in and surprise her? At my 7 year old son's school, mystery reader, usually parent or close relative, comes in at the end of the day to read a picture book, and after the story is over it's dismissal and parent takes their own child home. That would be great in your case especially so you don't have to say goodbye a second time! Maybe you can chaperone a trip?
Ask the teacher if there is someone in the class with a family situation like I described, or if there's a book or video program she might have seen. She might need help in realizing fiction is fiction, and in knowing you take really good care of yourself so that you are as safe as you can possibly be!