This one is not passing the smell test. “Bless you” is a very common response to sneezing and is more cultural custom than religious expression, the teacher is surely not ignorant of that. I also doubt a teacher would use the phrase “godly speaking” that is so stilted and contrived sounding. I think there is more to this story.
It’s possible this teacher and student have a history of clashing on religion in the past. And at this time one of two things happened:
The student said the phrase “bless you” very loudly to get under the teacher’s skin or
The teacher is using this as an excuse to nail the student because before this the teacher wasn’t able to catch the student in anything that could get her in trouble.
It must be one if these two scenarios because as you pointed out the phrase itself is quite ubiquitous and I dare say non-religious. No one ever takes it as a moment of prostelyzing.