There's the simple:
. . . how you asked me to use a bow and arrow . . .
However, assuming that there was an object that had been shot at (lets assume it was a tree), I think it would more naturally be:
. . . how you asked me to shoot that tree with a bow and arrow . . .
To expand on this, you say that you shoot a gun or shoot something with a gun but you don't (normally) say that you shoot a bullet (from a gun) or shoot something with a bullet (from a gun).
As far as phrasing goes, bow and arrow is used in the same type of way as gun.
Update: As per a comment, these would be more the more common phrases used in the absence of each weapon's direct object:
I was taught how to fire a gun.
I was taught how to shoot a bow and arrow.