One of the beautiful things about riding a bicycle around town is finding a little "cut-thru" to allow you a more direct route to your destination.
It is not always easy to find a cut-thru or a pathway like this. Typically, google maps doesn't know about them. When you use google maps for bike routing, you'll miss this. The two best ways to learn about a cut-thru is to ask people who already bike in the area. They will be your first go-to source of information about tricks and tips to biking. The second way is simply to get on your bike and go explore.
Here is one little cut-thru that I use to get Timmons Lane.
Timber Lane. There is a little pathway to the left of the tennis courts in the River Oaks Park. This is a pedestrian pathway so if you see someone walking there, please dismount and walk your bike. It's always best to be extra courteous when biking your city.
Once we get through the Timber pathway, we enter a parking lot. From there, we cross westbound lanes of Westheimer to enter the left turn lane for Timmons. From there, we wait for a opening in traffic and then turn left onto Timmons. The pavement on this section of Timmons is very rough. Be careful. Also, be aware of cars entering the Whattaburger and the parking garage for the private club. Other than that, it should be smooth sailing.