If you are bent on going to the bharatpur area during early August..you'll find the local resident birds for sure (you might have to walk into the bushes a bit ).
migrant and water birds would be few.
An intersting area at the national park is to get off the entrance path before the lake area starts and venture into the trees (a bit deep) and you might come across raptors.
Depending on how many days you have free at delhi and also on whether you can move out of delhi for these days, an alternate would/could be to drive out toward the north ...
1....
"Assan through Dhalipur power house. Assan Barrage Bird Sanctuary is located about 40 kms west of Dehradun, in the west of Dehradun valley on Dehradun-Paonta Road. Assan Barrage Bird Sanctuary is famous for bird watching. The Asan Reservoir is a small man-made
Assan Barrage Bird Sanctuary India
wetland of ca. 4 sq km area, located 40 km west of Dehradun, in the west of Dehradun valley on Dehradun-Paonta road. The barrage is 287.5 m long, the river bed being 389.4 m above sea level, with minimum and maximum water levels respectively at 402.4 m and 403.3 m. The Asan reservoir exists throughout the year and is fed from the river Asan and the discharge channel of Yamuna through Dhalipur powerhouse. Although the water level is controlled, it often goes down, and swampy islands in the middle become visible, attracting a variety of marsh-loving birds like Egrets, Herons and Lapwings, etc."
2...You'll have to spend the night at above..following day (early morning)head to a place called "renuka jheel" ..small santuary with ..theres a small 2 acre lion reserve ....plus local birds. post lunch head out of here to a place called kasauli so as to reach by nightfall..along the way look out for bird surprises ..at places the drive can be rough and bumpy.wake up in the morning to bird sounds and sightings of ..sun birds, warblers,bablers,koels,woodpeckers,magpies,white-eyes,bulbuls,swallows,nuthatches,minivets..and more if you are lucky ...this should have made your day...stay another night or head back to delhi (seven hours drive).
3... hit kasauli direct and enjoy the pine-altitude and everything it has to cool you off from the heat and dust of delhi.
If you need more details let me know..some firmed up dates and already fixed up itenaries would be helpful.
regards.