A snarky response would be to not just scout but use your uber ninja to sabotage their army. While they're stuck in your territory suffering attrition, bypass them and capture their capital. Then their stack disappears in a puff of magic.

Another idea is to fight cheese with more cheese. A great counter to enemy bow ashi spam is to simply spam more bows of your own, preferably in a bow maker province. The umbrella of death that comes from a dozen bow ashi units will often rout even samurai before melee contact.