It is not mandatory to perform a full Shradh immediately after Asthi Visarjan. The primary focus of the Asthi Visarjan trip is the immersion itself.
However, it is common and considered meritorious to perform Tarpan (water offering) right after the immersion at the Sangam.
Some families choose to perform a simple Pind Daan or a brief Shradh ritual on the banks after the immersion, especially if they have traveled from far and wish to combine the rites. You can discuss this possibility with your Pandit. The main, detailed Shradh rituals are typically performed during Pitru Paksha or on the annual death anniversary (Tithi).