Another yay for Castlewood. I know you're really really psyched to be mountain biking and I'm always psyched to see another chick out there but please please please wait until it's drier. I doubt you on your own are doing much damage but when you consider how much dirt you are bringing home and then the number of other people who are tempted to ride and bring home same you can prolly see how that would affect the trail. I'd sure hate to see trails closed off to bikes.
Once you get comfortable with a little singletrack (and we finally dry out) you could also try the Love trail as has been mentioned or the lower part of Chub trail from the parking lot by the train tracks over to the hill that would take you to Lone Elk or Lost Valley or Brommelsiek or even Queeny Park's outer loop. Some of these trails dry a lot quicker than those floody river bottoms trails do. Also, I haven't had a chance to ride with them in the woods but the St. Louis Adventure group rides Castlewood on wednesday eves and some profess to be beginners. GORC- Gateway off road cycling- does some beginner rides too.
Remember, horses and hikers have the right of way. Pass sensibly. If you ever see a chick on a mtb tandem with a little kid say hi and join us if you want. We don't care about speed (we aren't all that fast anyways) so long as we're having fun and we don't care if you have to walk some stuff either, we all did our share of that and still do, in some spots!
I used to have an open mind but my brains kept falling out.