Since you provide only limited info to go on, if I had to guess, you would find the bridge at the GPS coordinates of 36.818823,-119.341822 . Copy and paste the coordinates into Google Maps and see the satellite view. It shows a narrow bridge that has closed (see the white barrier on the SE side of the bridge). The road (Pine Flat Rd.) leads to what appears as a campground on the south side of Kings River SE of the bridge that crosses the river below the dam. The bridge crosses Mill Creek which is a tributary of Kings River. From your picture, the bridge doesn't appear to cross a river but a stream.
My guess is after the store, you went left and crossed over the river to the park for lunch then went east Elwood Rd to Pine Flat Rd (the one on the south side of the river). It appears you should have taken the Pine Flat Rd on the north side of the river (via Trimmer Springs Rd) then crossed the river at the COE office.
If you think this is wrong (remember my disclaimer!), it would help if you could give more detailed info as to how you got there. For instance, if leaving the park we turned right onto Piedra Rd. then left onto Elwood Rd. The bridge we know was before "X" and after "Y".