I was in this same boat about a month ago. Braes Bayou trail is not that great for cycling. Terry Hershey/George Bush is much better as you have to cross zero roads, although I imagine on a weekend, like any hike & bike trail, it can get pretty crowded (so far I have only ridden it on Fridays). Caution: George Bush trail
floods after a moderate rainfall.
Here is one website which has basic info including this map of the Terry Hershey trail:
PDF of Terry Hershey Park
What it does NOT show is the connection to the George Bush trail, which is west of HWY 6. To get to the George Bush Trail, once you cross HWY 6 and come back up to street level, you will soon come across a north-south path. Take that north, which after a quarter mile or so will then curve west. Once you hit a road, then take that road south, which after half a mile or so will dead end into the start of George Bush trail. All total I think the round trip is 36 miles.
I live at the west end of the Braes Bayou trail, and to get to Terry Hershey Park trail I drive Beechnut west to Beltway 8, then travel north on the Beltway 8 feeder roads to a parking lot for the trail. The lot is north of Briar Forrest Drive and Beltway 8, and just north of Briar Hill Drive (a smaller street). Red arrow shows turn into the parking lot. Green shows the bike path. It follows the Buffalo Bayou.
As for other routes around Houston, click the "Training" tab in the left column of my
cycling team's website for other cycling routes around Houston.
PM me if you have other questions.