How to safely restore the white to the vintage wedding dresses depends on the fabric. It also depends on your budget, professional restoration is pricey and skyrockets the more detailing like beading, flounces, netting and/or lace, etc, there is on the vintage wedding dresses.
Because even the ‘simple cotton vintage wedding dresses’ will usually have fragile detailing like embroidery and/or beading, it’s best to do this by hand in a sparkling clean and well rinsed bathtub. The large space of the bathtub will ensure plenty of room for the many yards of fabric in even the simplest vintage wedding dresses to be completely covered with water-the fabric should be able to float loosely during the soaking and washing. Use a very gentle squeezing from neckline to hem, over and over and over again to work the soap and whitening agent through the vintage wedding dresses. Drain the wash water, gently squeezing the excess soapy water as the water drains. Refill the tub with cool water and gently swish and squeeze the vintage wedding dresses in the rinse water-repeat the draining and refilling the tub until the rinse water is no longer soapy when you gently swish and squeeze the vintage wedding dresses. Squeeze as much of the excess water as you can from the vintage wedding dresses, then put sections of the vintage wedding dresses between thick absorbent towels and press to remove more of the water. Then place the vintage wedding dresses on a flat surface out of the sun.
If the modest vintage wedding dresses are silk, natural fiber satin, or a synthetic like polyester, rayon or taffeta, really your best hope for restoring the white is a professional dry cleaner who specifically advertises expertise in restoring antique and vintage wedding dresses. Again, this can be an expensive option but is the best and usually safest way to ensure your vintage wedding dresses are wearable for your wedding.