Soltaro is correct. There is almost no synergy between Expert Marksman and Man-At-Arms. You need a weapon equipped to use most Man-At-Arms abilities and swapping weapons takes 2AP.
The only possible exception might be swapping to a melee weapon, using Rage right before a fight, then swapping back to a bow. The Bow DOES GET THE DAMAGE BONUS from Rage... but you need Strength 10 just to have a 100% chance of Rage working, so blaaaah to that.
