Use Bounding Strike to both chase and escape, but it could not be used to dash through walls.
Determination could also be used for those purposes, but even better for chasing due to its cooldown reduction.
Try to loop behind the enemy team then push a priority target into your team with Comet, preferably knocking up other members of the enemy team on the way.
It is possible to use Bounding Strike at an angle to get ahead of your target, and then Comet them backwards into your team. This, however, sacrifices the damage and knock down of Bounding Strike, unless there is another enemy champion behind your target. Remember, she knocks down and stops at the first enemy champion hit.
While not mentioned, Comet could only be used on enemy champions.