There's no such ability and I don't think it is possible to create one like that accurately.
You can increase hero's attack speed either when he:
a) attacks -> this can be abusable, as you can stop the attack and start it again, thus he would gain the bonus quickly
b) damages enemy -> however there is a delay - the time when he shoots the arrow and the time when the arrows land. The good thing is that this will not be abusable.
Then I think you could add an invibile ability (e.g. gloves of haste with levels) and just level it up to give the feeling of "bonus speed" (though I did not test if leveling up gloves of haste when they're on unit will increase the attack speed).
And you would need to keep track of when hero has activated those arrows and when not, so you won't increase his attack speed when he does not shoot those arrows.