Actually the hybrids are capable of reproducing or backcrossing with both parent species. However due to their hybrid nature their eggs are not really setup for success. So the chances of an F2 or backcross outside a hatchery are next to nil.
Stripers migrate into rivers (like salmon) to spawn. Their eggs are buoyant so they can tumble down the river until they hatch. This keeps them oxygenated until they hatch.
White Bass are similar but their eggs are adhesive and not buoyant. They attach to vegetation or rocks in rivers or windswept areas and the flow keeps them oxygenated until hatching.
The hybrid's eggs are not buoyant enough to tumble in the current like a striper, and are not adhesive enough to properly attach to rocks or vegetation. They sink to the bottom and become covered in sediment. This results in rapid suffocation.
Despite this, the states of Maryland and Virginia no longer stock hybrids in water with drainage access to the Chesapeake bay for fear that the hybrids will get out there and destroy the striper gene pool.
To answer your question I would try when the white bass spawn. Mid-March - late May; at water temperatures of 12-20 degrees C.