If your sister suffers from intense social anxiety, then picking out a wedding dress is going to be a big deal for her. She's going to be nervous about her upcoming wedding, and shopping for the dress (with all of the sales staff, and changing required) is going to be a major stressor. So, you should go along and help make it more relaxing. You can also plan out ahead of time some key points so that she doesn't get too overwhelmed, or embarrassed. Here are some things to plan out for when you go along with her and try on bridal gowns at a place like Eduardo's.
Hit The Bridal Store Early
You want to show up to the bridal shop early. Ideally, you should be the first women there. This serves two points. First, the staff won't be weary of dealing with many other bridal parties that show up through the day (some of whom might not be too nice to the salespeople). You don't want any of that residual bad energy to be hanging around. Secondly, your sister will feel more comfortable in a less crowded and hectic store.
Bring A Digital Camera
You want to take photos of the various outfits. She might be so nervous that she doesn't quite remember what each looked like. So, even though she tried on the dress, a few dresses later she might not recall if the cut was what she liked. A smartphone (or digital camera if you don't have a smartphone) is essential. You don't want her to have to go back and try on the same dress over and over, it will frustrate the sales staff and drag out the day which will stress out your sister.
Narrow Down The Silhouette Style Beforehand
One great idea is to select the silhouette style beforehand. This way she doesn't have to try on dresses that she knows she doesn't like. This is especially important if your sister is not super into fashion and hasn't been looking in bridal magazines at the different cuts and styles. You could create a small arrangement of photos and show her the different styles and she can show you the ones she likes, then you can speak with the saleswoman and discuss the dresses.
Don't Bring All Her Friends
Definitely don't bring all her friends. You don't want the day to turn into a Kristen Wiig comedy. The more people, the more room for something to go wrong. There is no need for a whole party to show up.
Pick Out Nice Bra and Undergarments
You don't want her to be embarrassed, so remind her she's going to be in and out of her clothes for a large part of the day, with the saleswoman helping her dress. So, if she's a fan of thongs or granny panties, she might want to reconsidered and go with something like bikini panties.