Copyediting a book is a complex process, and the cost of having it done professionally can vary drastically from one project to the next. The number of pages, the difficulty of the material, and the speed required all play a role in determining the cost.
Generally speaking, roughly 2–4 cents per word is a good starting point for budgeting a copyediting project. Often, editors will offer an hourly rate (which can vary anywhere from $30–$50 an hour, depending on their experience), or a per-page rate (generally $5–$11 per page). It may also be possible to negotiate a flat fee, so it is always worth asking.
No matter what rate you end up paying, it's important to remember that you get what you pay for. It's wise to compare quotes from multiple editors, read reviews from past clients, and really evaluate who you are comfortable working with before making a decision. A good editor will save you time and money in the long run and make your book the best it can be.