Since I was once in your situation, (actually EVERY ONE of us was in your situation at some point) I can tell you, the fear that you have of riding in a group is more in your mind than reality. It is a good idea to start out on more beginner friendly rides just until you get some idea of your level of fitness. Nothing more humiliating than realizing you have bitten off more than you can chew as you huff and puff along while you watch the rest of your group get smaller and smaller as they ride of into the horizon. (Guess how I know?)
Another suggestion that I have personally done is the beginner ride at Richardson Bike Mart. I know it's a bit of a hike from Irving but you can take the Bush to Coit then go south to Campbell. It's ~11 miles total with a stop at a convenience store at the turn-around point. The leader, (when I rode it) was very patient and makes sure nobody is left behind. Even if that means stopping the group to wait on 1 person. I rode this when I started out then came back to it with my wife when she was starting out. Coming back to it was PAINFULLY slow, but it was the pace the group could maintain. She will even call for one of their store support vans to come pick you up if needed. (On one ride, a lady swerved into the curb and came over her handlebars. She wasn't hurt, but she was done for the day. A van was called and she rode back to the store.)
Like others have said, the main thing in a group is holding a steady pace and keeping a straight line. Weaving back and forth is not a good thing!
So, in summation, realize your fears are largely imagining things to be worse than they are; find a good friendly ride; don't wait around--get out there and do this already.