Enterprisingly is the adverb: you do something in an enterprising way. You see a gap, you try a new idea, and you make it happen. The word is rather rare in speech; people more often say “she was enterprising enough to…” or just tell the story without the -ly. When it does appear, it is usually in writing, and it still carries that note of praise — resourceful, not reckless. Use it to describe how an action was done, not the person as a whole; the person-word is enterprising.