Good question - I have not found much mention of billmen in my reading around this period, but I think the habit of the day was to emphasis the role of the higher status troops like knights. In Heath's book Armies of the Middle Ages, he mentions one of their earliest appearances was at Formigny, 1450, but they can't have made a big contribution to the extent that the English lost. Heath says there were around 25% of the infantry in the War of the Roses, the balance being archers, and were present in thousands at the climatic Battle of Bosworth.