Can you change a straight edge to a rounded or bullnose edge on a stone countertop after installation?

I would recommend against machining your top in-place. Bullnosing a top requires removing a lot of material, and then the nosing must be polished to match.
This is not a job that is easy to undertake in the home, and uses a polishing head like this:

Profiling head for nosing stone tops – Available on Amazon, and specialty tool supplies.

Replacement may be the best option here, unless you have a contractor who really knows what he is doing, and will bring a lot of drop cloths, plastic covers, a strong wet vac, and a lot of chops. And be prepared for a ton of dust in your home.

A possible option is to add a bull nose to the edge, but be aware that the bullnose would be fragile until it was glued in solid, and requires special tooling to cut and fit it in.

3/4x12 Light Cream Limestone Pencil Liner Wall Trim Tile
This is a tile trim from Amazon. it can be used as an edging (if it matches or contrasts nicely). Your marble fabricator may be able to make 1/2 round trim from the same stone as your top. It may need to be pieced, but can give you the edge you want without the mess or rework your looking at.Talk with your contractor, see what you can come up with.  
I hope my suggestions work for you, Keep in mind that countertop edges are easy to choose and hard to change!
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