Can we patent a process?
Definitely.
35 USC 101 provides (emphasis added):
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Is the service you describe a patent eligible process?
Not every process can be patented however. In particular, it must not be "abstract". There is no hard rule for what is abstract. However, methods for financial trading (for example) are typically not allowed.
Because you can't share precisely what you're doing, it's impossible to give you a firm answer. However, since you seem to be doing something to a physical device, then your process is probably not abstract, and so would probably be fine.
Costs
It's impossible to give you an answer here, since it depends on the nature of your invention and who your attorney is. It wouldn't be less than about USD 5000 for the patent application preparation and prosecution though, I would think.
What should you do
Go talk to a patent attorney. You will be able to disclose all the details of your invention to them, and they can give you a more accurate opinion of its patentability, along with a cost estimate.