I can understand the hesitation not to reveal your idea. However, the chances of someone around you hearing the idea, then having the time and resources to execute that idea faster and better than you have is very slim. As others a have said, You will not be the first person to have that idea.
In fact you may find that telling people your idea could help you significantly as those people around you may be able to help you with ideas or introduce you to key people.
Ideas are the easy part, execution is the only thing that matters.
Share the idea and see that it will only help create discussion. You will find people will question your ideas as well which is good, so don't be nervous of that either. Often the people that will be most pessimistic/ challenge your idea are the people closest to you. Embrace it.
Set up a business plan and basic idea before telling people (as I imagine you have) then get started on the execution.
Hope you make the right idea and that the execution goes well! Good luck!