At the 1995 Rugby World Cup in South Africa, Bevan was in charge of three matches, including the opening match of the tournament and the semi-final between hosts South Africa and France, and was one of the touch judges for the final. At a banquet held after the conclusion of the tournament, the president of the South African Rugby Union, Louis Luyt, described Bevan as "the most wonderful referee in the world" and "the outstanding referee in the World Cup" before attempting to present him with a gold watch estimated to be worth £1000 GBP. Bevan's response was to walk out along with the other officials present, and later said "'It was something I could have done without...It could be misconstrued, and if that is the case, it leaves a bitter taste." He refereed three games at the 1999 Rugby World Cup, hosted in his native Wales, including the semi-final between Australia and South Africa.