This month I discovered that there is a women's shooting club that meets the 3rd Sunday of every month (or 2nd?) at the Winchester Gallery here in Fort Worth. I went to this last one and it was really fun. They're very non-competitive and shoot fun targets and it's a feel of just doing the best you can and enjoy the company. And then there was cheese and fruit trays afterward with champaign while we had little recognition awards and whatnots. It was super fun! They will not be meeting in December due to the holiday but will pick back up in January. I highly encourage you to call Winchester and sign up early as space is limited, it's $16 and you use less than 50 rounds, they also allow .22 caliber to be used. I will definitely be going every time.
I also found out about Diva Wow while I was there, it's a women's outdoor club that does a variety of activities, not just shooting but also hunting, archery, dog training, fishing, AR-15 clinic, all sorts of different things.http://www.divawow.org/