I am adding a bathroom on the back of my house. My house has a crawl space under it and no basement. Te crawl space goes part way under where I am hoping to do the bathroom and it also backs onto the existing bathroom. What kind of cost will it be for someone to install plumbing for this space? Also, at what point do I call someone for a quote? Should I do this first

Get your desired lay out try to lay out to adjoining bath service mechanicals save Mat/labor
Call plummer
Get 3 quotes
Check his pluming License and Insurance
How long in business.
Get three Ref from him
Get a written quote and written quote for hourly rate for extras
Ask about guarantee and warranty on parts and labor.and have it writing
Contract start time and finish date in writing
Cost is relative In my area a complete very basic bathroom runs 6.000 to 12,0000. Plumb $2,500 to $ 4,000 labor only
Crawl spaces are tough to work in more labor. Keep in mind good insulation and freezing pipes. Try to lay out your tub toward water lines and an inside wall for access later/service Avoid frozen pipes locations. I do not approve of tub waterlines on outside wall no access and pipes can freeze.
I hope this helped Signed 21 Boat
Happy Holiday

My 2 cents:

Professional Plumber prices new fixtures installation As Per Fixture. So, you could get approximate price over the phone. Prices depend on what part of country you will be building in and what materials your plumber will use. But figure waste, vents, h/c water + setting finish should these days run you bet. $1,500 to 2,000 per fixture. You supply all plumbing fixtures.