I would not use saunter. It so casual. No sane woman would saunter, she would be so pleased to be going through an important occasion to be so relaxed. You could say "marched" down the aisle, "half-stepped" down the aisle, or any number of verbs indicating the result, without a phrasal verb.
"Saunter" does NOT mean "walk graciously", or even "walk gracefully". A woman who has been divorced 42 times, and who is now taking her 43rd husband (whose name she thinks she remembers), might "saunter". I can't imagine most women, however, walking down the aisle in a way where the word "saunter" would fit.
Thanks to all of you!
Now I've got it clear, and you're right, sdgraham, sometime dictionaries don't explain as well as, say, GreenWhiteBlue's explanation.
I think I'm going to stick with mommamia suggestion: glide
Have you ever noticed how you can almost identify someone you know by the way they walk? That's because a person's natural walk is unique to them. Everyone has a variety of walks they employ, depending on their prevailing mood or attitude at any given moment.
If you decided what mood you want your bride to have, then you'll know what kind of word to use.
It sounds like you want her to be sedate, ladylike, and classy. A woman with those personality traits would glide down her wedding aisle. A shyer woman might follow a very normal movement and just walk down the aisle. A woman who was not-too-graceful could possibly look like she's marching down her aisle.
A bride could bounce, skip, sashay...there are lots of inappropriate walks she could use if she were that kind of woman.
A bride who drank too much champagne beforehand and had to squint to see the priest would stagger or stumble down the aisle.
Saunter: That would be one blasé bride! She'd wander around, yawn, and "get to the front when she got there" type of thing.
If the bride is being accompanied by her father or both parents, you could say she was escorted down the aisle.
Figure out what kind of person she is, what mood she's in, and how sober she is. The word will jump out at you.