No, you can’t recycle bowling balls. Bowling balls are made of polyurethane and liquid plasticizer with weighted cores made from polyester resin filled with varying amounts of calcium carbonate, barium sulfate, and glass microspheres.
Want to learn more about how they’re made? [YT link, text here.] If you still have a burning desire to know more about bowling balls then InsideBowling has a three part video series on the history of bowling balls. (Part 2, Part 3)