I would would like an ancient Roman/Greek style bust made of someone I know's head?

Is there any businesses out there that specialise in this?

If so- can it be done with photos or only in person?

I am sure there a larger businesses which do this, but it will be more personal and you probably get a better response if you talk to a local artist. I'd first check the yellow pages if there is a local sculptor listed. Also if there are sculptures in your town you like and which have been put up not too long ago, you can usually easily find out who made them.
The next option is going to a gallery exhibition which includes figurative sculpture and talking to people there. If you don't like the style of the things there, you probably would get the name of other possiblities.
As far as photos are concerned. If it's only a single photo it probably won't be really good. With a number of different views of the same person (at least front, side and back) it may be OK. A person would be easier as some people like to take measurements.

Shark City Click (Fam-Lay) - Head Bust ft. Pharrell Williams (Fast & Furious (4) Soundtrack)