The floor around the tub would need to be sloped toward the drain, and you'd probably want a curb. By the time you took the tub out to build this, you could probably put in a new tub/shower. I suppose you could dump the tub's ouput into the new shower drain, but cleaning underneath could be a pain as well. For a shower, the drain is supposed to be 2" vs. 1.5" for a tub as well, so you may have to tear up some other stuff. Suggest you live with that tub as is if you want to keep it, or chuck it and put in something new, done right.
But, I'd keep an open mind for other suggestions.