I haven't been asked about a bikini line on a girl that age, but if they were quite hairy then i can understand if they want a very basic bikini line. I would definitely do the other areas first and then check that they were still happy to have it done.
I'm quite hairy myself and remember doing my legs when i was about 9 or 10 because i was so self-conscious about it. I was an early developer.
I think if possible it is best to avoid shaving because the hair comes back so much more noticeably than waxing and causes that stubbly feeling. Also, girls can sometimes shave places that don't need shaving, such as the thighs and then the growback means that quite often they feel they should keep shaving to get rid of the stubble. If they are coming to a professional, they can learn what to do and not to do. I know some people will say this is the Mum's job, but often they don't know themselves or their child can feel a bit shy about talking this over with them.
I shaved for years and wish i'd known to wax sooner xx