Before you visit a, you should think about any relevant dress criteria. Is your wedding a formal winter wedding or a relaxed spring summer wedding? Are you marrying in the morning or the evening? Your dress should reflect the type of wedding you are planning to have, a flimsy slip dress at a black tie affair would be as out of place as a hoop skirt with a long train for a beach wedding.
There are a few restrictions on style and colour nowadays, so white is as optional as it is acceptable. However, if a cocktail length skirt or a Tiffany blue dress might be upsetting to your grandparents, but I say the decision is yours. If you are getting married in a church, be sure to ask about restrictions and requirements, such as a ban on bare shoulders or hair coverings.
When it comes to shopping for the dress itself, your mother does need to be invited if she is helping you to pay for the wedding dress. What she can’t do is force you to choose a dress you don’t like just because she is paying for it.