It's going to be very difficult for you to do this. Contrary to some of the other answers, you can't patent an idea, only a design or process. And even if you turned your idea into a working prototype, the process of patenting takes many years, can be expensive, and is not guaranteed to be given. Even with a patent, trying to enforce it is next to impossible unless you are have expensive lawyers. I have a patent I am part of through a former employer, and it's been useless for me.
Companies don't often take ideas from outsiders, and even less rarely will they sign a Non-Disclosure Agreement on an unsolicited business idea. The problem is, most ideas in a business-sector have been thought of. Say you are pitching an idea to banks. There are 100,000+ people working in the banking sector in America. Your idea has probably been thought of before by one of them, even if the company decided not to go implement it.
Here's what I would suggest you do, in order of chances of success:
1) Just go ahead and do the idea yourself. If your idea is "soap, but in the shape of cute animals", go and make cute animal soap. The process of making your product might get the attention of a competitor in the space, and you could be acquired or go into a partnership with them.
2) Get hired by one of them. Sounds like you have a target list of companies in a business sector that you want to sell your idea to. Your second best plan then is to make a targeted attempt to get hired as an engineer there. Contacting their HR dept, finding friends who can get you contacts, applying for jobs posted online... If you actively seek them, you will get their attention. Having an active interest in their business and ideas for improving products are very attractive to companies when mentioned in an interview.
3) Finally, if you can't start your own company as a competitor, and don't want to get hired by them by the normal route, you could try to pitch them your idea by sending it to the head of their engineering department. But again, the chances are quite low. Its very easy for them to be able to truthfully say "we had this idea 5 years ago, but haven't implemented it yet." There is no protection from that.
best of luck.