The effect of “Bountiful Artemis” is a Continuous Effect, and cannot be chained to. You will draw 1 card immediately after a Counter Trap’s effects have resolved.
Your “Bountiful Artemis’s” effect will activate even if your opponent is the one who activated the Counter Trap.
If “Seven Tools of the Bandit” is used to negate the activation of another Trap Card, such as “Magic Jammer”, you will not draw a card for “Magic Jammer” since its activation was negated.