I believe you will have much better luck in approaching the sale of your idea in a different manner.
An angel investor is not looking for the next best "mouse trap" or any other invention. Understanding the angel investment business is part of the difficulty you may be having, and why there is no interest at this point.
Angel investors are looking for a team (meaning more than you individually) that can take a product from the idea stage to manufacturing to selling in the final market. If you have no experience in running a company or a major area of a company and if you do not have the people, then the best idea is of little interest to an "angel" investor.
You would be doing yourself a disservice to hire a business planner at this early stage if you have no way to raise capital, create a team of experienced business people, and generally be able to take a business plan to reality. Anyone will be glad to take your $10,000 and write you a plan; but with no way of following through, it's just as good as last week's newspaper.
If you have a great idea, consider the more appropriate approach of selling your idea to a company that can make and sell your product. You don't have to do anything, but license the rights and collect a fee, either a one-time fee or an ongoing royalty.
There are many patent attorneys that are aware of companies that purchase patents, as well, you can search for a company that specializes in inventions.
Your cost to investigate these options is a mere fraction of what you would pay to your "business planner".
From your perspective, you are trying to build a stadium, build a new team, then hit a home-run. Instead, concentrate on the pitch in front of you, and hit a single. All you need to do is make that little piece of paper with the patent stamp on it turn into some cash for yourself. You don't need to try to make a million dollars on the first try.
Good luck on your endeavors.