Her name is Sofie and was performed by Alice Dinneen.
She was added as a neighbor in the second season.
For those of you who dont know, Big Bag was produced by CTW for Cartoon Network and lasted 2 seasons.
When I interned at CTW 5 yrs ago, I got to look at the whole Big Bag library and had the chance to try on Chelii and Sofie before they were packed away. I really never had the chance to follow the show on CArtoon Network but after watching it, I became very fond of the charcters, especially Chelli (as you can see in my nick) who was wonderfully perfomed by Joey Mazzarino. There is a Chelli doll that was made, and can probably be found on eBay, if your a collector, as well as a hand ful of VHS tapes put out by WB. I have a few on tape myself, including Elmos Visit.
If any one wants to chat more about it, I'd be happy to answer any questions.
Hopefully Chelli and Sofie can pop up on the top of the Home Page from time to time, since they are the forgotton Muppet family Members
Mike