Jamison Ross drums his way to victory in the Thelonious Monk International Jazz Competition. (Evelyn Hockstein for The New York Times)WASHINGTON — Jamison Ross sauntered onstage at the National Museum of Natural History here on Saturday with the solicitous gleam of a casino floor manager, his bulky frame encased in a suit and his face bearing a wide-open smile. Graciously, he initiated a round of applause for his fellow hopefuls in the 25th-annualThelonious Monk International Jazz Competition, and another for the event’s unflappable house band. Then he sat down, picked up a pair of brushes and counted off “Bye Bye Blues,” an uncomplicated song recorded by dozens of American entertainers from the 1930s on.