You are essentially talking about creating an undermount tub out of an alcove tub, which would be fine if you wanted a tub only usage from it. If you want to use it to shower, then anything you place on top of it has to slope to the inside of the tub so that the overspray runs back into the tub rather than all over your floor. You're not going to be able to bend a slab of stone to do that. If you do use the slab for the apron, then you will have a seam at the top between the slab and the tub. That may not be that attractive and wil need to be kept caulked in order for water to not penetrate it and cause damage to the subfloor below.

Thanks Green Design. This tub is definitely used as a shower...only full bath in the house. Sounds like my dreams were bigger than reality. C'est la vie.

I have a question? How do drop-in tubs with showers avoid this problem then? Wouldn't they have the same issue of water hitting the edge/sides?

Anyhow, I would google and do some more research before negating the possibility of this working.

Here is a link to a GW post with pics of what you're contemplating.

Here is a link that might be useful: alcove tub

Drop in tubs are unsuitable for use as a tub/shower. They are designed for tub use only. A tub for a tub/shower has an integral tile flange that is covered by the wall cladding to direct the overspray back into the tub.

If I were you, I'd replace the tub. There is no longer any process that is a true "reglaze" of the tub where it is refired and liquifies the porcelain like the original process. All that is currently possible is a heavy duty paint. That will eventually fail. Many sooner rather than later.