I avoided Tribble at first because of all the climbing, but have grown to really enjoy it. I feel like a kid exploring a maze

! It is quite scenic, with lots of exposed rock surfaces you can ride over, not to mention the lake. There are trails not shown on the attached map connecting the "bare rock surfaces". And there are actually fast, level trails too if you know where they are.
For group rides, look at sorbagatr.org and the Apalachee Cycle Facebook page.
However, I found that I didn't learn how to navigate the park by following someone else. Set out on your own when you don't have to be back at any particular time, and have fun exploring. You won't get seriously lost -- it's a small park -- about one mile by air from one end of the trail area to the other. It's hard to get in a 10-mile ride. Worst case ride downhill to the lake, ride around until you get to the dam, and from there to the road, which is where Buster recommends parking. I sometimes leave Strava on, and refer to it at intersections so as to ride as many new sections as possible.
Noting a few landmarks as you drive thru the park helps. After you cross the big bridge and head up the hill and cross a pedestrian crossing, Chandler Lake -- the lake with the trails -- is on your right, a couple hundred feet back in the woods but not visible from the road.
Continue on and there is a gated dirt maintenance road to the right. The trail crosses this in a couple places. The "main" trail between the maintenance road and the lake area will be some doubletrack coming off the right of the maintenance road, between two boulders (another good landmark when riding).
Turn right a the 4-way stop. You cross a small bridge. The playground is on the left, and the trails on the right. (I believe this is the "official" trailhead. There is a hinged trail-closed sign on the corner, and this is where the group rides meet.)
Hope to see you there!