I have never played the Bioshock games, but Little Sisters still don't fail to creep me out.
The colors and patterns on the dresses are varied in the game, so I couldn't really go wrong with the fabric choice. However, I chose to go with the purple/lavender-striped design shown in most of the concept art and found a medium-weight linen of that exact pattern and color online. I was happy to discover its rough texture and slightly heavy weight when it came in, which is perfect for a genetically and mentally mutated child running around in a dystopian nightmare landscape. The attached apron, collar and sleeve cuffs are made of white muslin and perfect for absorbing grime and bloodstains. Four decorative buttons complete the dress.
The design for the dress was fairly simple, based off the dress pattern I used for my Ponyo dresses. The original pattern is collarless, so I took the Mandarin collar I made for Ponyo's normal dress, flipped it upside down and added a half-inch all around to create a Peter Pan collar.
The apron was created by first making a mock-up of bodice and sketching out the arches on the top of the bodice. Then I cut it out and used that for the bodice of the apron. The skirt is the same as the skirt peice for the dress, just shortened. The top and bottom edges are trimmed with black bias tape and the apron strings were free-based. While the bodice is sewn directly to the dress bodice, the apron and dress skirts are attached separately, which makes the apron poof out independently of the dress skirt.
The apron is attached to the dress to make the costume all one piece, so all my client has to do is zip it up, tie the strings in a nice bow and go creep people out.