The bride's elegant dress reflected her good taste.
Here, we can see her good taste in her choice of dress. Her good taste is the cause of her choice of dress. Because she has good taste, she chose this dress.
The bride's elegant dress is a reflection on her good taste.
Here, her good taste gets augmented by her choice of dress. Her good taste is a result of her choice of dress. Because she chose this dress, she has good taste. This does actually seem a strange thing to say.
The bride's elegant dress is a reflection of her good taste.
This is a perfectly fine was to express the first sentence. Again, the good taste is the cause of her choice of dress.
A student's grades reflected her teacher.
Because the grades are good, we know her teacher is good -> the teacher caused the good grades.
A student's grades are a reflection on her teacher.
Because the grades are good, we think of the teacher as a good teacher -> the grades caused the teacher to look good.
A student's grade are a reflection of her teacher.
Again, the same meaning as the first option -> because the teacher is good, the grades are good.
A is a refection of B means that we can explain that A is something (good or bad) because of B. A reflects B means the same thing.
A is a reflection on B means that because A is something (good or bad), B will appear to also be that (good or bad).