Well done!
I live about where you started from (the gazebo/playground parking lot). So I ride from there all the time. I'm assuming from your post that this means GBP is no longer underwater?
Here's what it looked like last weekend as we tried to do our normal saturday morning ride
FYI, Fry Rd isn't the end of your ride. You can hop onto the Mason Creek Greenway and continue all the way up towards the Rudy's on I-10 feeder. Once on the greenway it also splits where the bayou splits and you can take a ~1 each way path out to where the Katy Bike Barn is, then come back and continue all the way up to I-10. From the greenway you can also connect to concrete paths that wind their way up towards Kingsland Blvd and beyond. The just built a new bridge over the bayou to make that easier as well.
I basically did this ride the other weekend. See if this loads for you:
https://www.strava.com/activities/831803668 (it might not because my acct is private i think).
If that doesn't work, here are some easy to see maps I made:
This one shows the end of GBP as you come to Fry Rd, and how you can get to the Mason Creek Gwy. I usually use the green route through the neighborhood as it keeps me from having to cross Fry Rd.
The path goes under all the roads, so you never have to stop. Once you keep going up it, you'll reach the split. This map shows where you can go.
If you want to explore some neighborhoods instead, as I mentioned there are concrete paths all through the area. I've highlighted them with the green arrows (the green lines are Google Map's biking, but that also shows roads).
Good luck, and have fun! I'll probably see you out there on the weekends. Myself and a few friends ride through the park and the roads out towards Katy Mills, and through Cinco Ranch and we've got routes to Fulshear planned too.
You may want to register for the Tour de Houston, and a few of the other fun T-Shirt rides that lead up to the MS150. They are a good time and they get you biking in areas further out from Houston. Great way to experience new areas on a bike. Bluebonnett Express is a popular one.