When it comes to professional cleaning services, price is just an excuse, and never a reason. What have you done to get this cleaning prospect invested into the discussion before you quoted the price? Have you gone over to see the layout of the location? I never discuss money over the phone without first seeing the location I'm expected to clean because that's how you end up with unpleasant surprises.
You always wind up underquoting or overquoting. One of our smaller customers is a massage therapy clinic with dozens of small rooms with lots of tricky furniture. I'm glad I didn't quote that customer over the phone for my cleaning services.