Wow--congratulations Michelle. I've been taking classes in Continuing Studies at Stanford for about five years now, so I should be able to give you some help since I'm on campus at least once a week.
Dress overall is what the above posters have said, very casual, but not even that--I have seen adults come to class in appalling rags. This might not be true for the business school, but then, you will be in Silicon Valley where the level of dress in certain industries is um--low. There are, however, a few who do dress quite well and I appreciate them. I had one woman professor last year who was a joy--I looked forward to class to see what she would wear. Her full-time teaching position was in another school at SF, however, so that may explain her chic wardrobe.
Overall I think it's fair to say that the dress is quite conservative in the sense that people stick to the casual basics. A few do dress better though, and I think you can find your niche in smart casual.
I do see women wearing heels occasionally, but the norm is flat shoes or low heels. If your classes are confined to the business building you won't have to do as much walking and will have more leeway, but there are a lot of uneven areas and people cut across open areas a lot. There are many cyclists on campus--you've got to be ready to jump out of the way if you are on a bike path.
I see a big variation on campus. I'm sure you will be able to find your niche and be comfortable and stylish. Not to mention you will be next door to Stanford Shopping Center--temptation!