I have been selling ideas for a long time, and decided to become a book packager (which I did before doing what I do now) solely because it's an industry that makes it possible to sell ideas.
One project took more than five years (selling Stanley Kaplan on creating a line of test prep books, finding a publisher and then creating them and launching the series) and one book took a day to invent, a day to sell and three days to write. I learned a lot of lessons the hard way--I got 900 rejection letters my first year and sold exactly one project.
Two things have to happen before a big company buys your idea:
1. They have to be in the business of buying ideas.
The book business buys ideas. The toy industry does, but only through a tiny number of agents. The car industry... hardly ever. Apple doesn't buy ideas, but they don't mind stealing them.
A company that likes buying ideas has a process. They make it relatively straightforward and they have no upside in stealing from you. A company that isn't in that business puts up barriers. They troll around trade shows looking for ideas to take (and there's nothing legally or morally wrong with that, imho).
Years ago, I invented the first fax board for the Mac. Our plan was to build a prototype and then sell the rights to one of the many Mac peripheral companies. The experience was eye opening. We talked with more than a dozen companies and had meetings with more than six. Some companies were clearly professionals at this, others were just fumbling in the dark.
I also invented a version of the wireless music player (sort of a precessor of the Sonos). We spent a lot of money and built a prototype and brought it to various hi-fi companies to license. One of the first stops was Polk Audio, a leading speaker company with direct mail experience looking for growth. It seemed a perfect fit.
We had a nice meeting, but I was sure we were out of luck before it started. To get to their offices, we had to walk through the factory. Polk is basically a furniture company that makes speakers. The entire culture was focused on cutting wood and shaping it into speakers. They had no experience or desire to make an electronic device off shore and market it.
Short summary: if you have an idea for a company that doesn't know how to buy it, move on. And if you want to be in the business of selling ideas, find an industry that has experience buying those ideas.
2. They have to trust you
This is far bigger than it sounds. Venture capitalists, for example, appear to be in the business of buying ideas. They're not. Far from it. They are in the business of funding entrepreneurs. The ideas are secondary, easy to find, not so important. The entrepreneurs, the ones you can trust to stick it out, to push through the Dip, to tell you the truth, to hire and lead and inspire... that is the scarce resource.
The reason that big companies don't want to hear from you is that they don't trust you. They don't trust you to understand their industry, or to understand implementation. They don't trust your judgment about whether it's a good idea. They don't trust you won't flake out, or sue them, or sell your ideas to multiple parties.
You may be tempted to seek out a middleman, someone they do trust, an idea scout. While I'm sure there are a few reputable people out there, in most industries, they're just scam artists looking to take your money. Again, in the book business it's different, there are reputable agents, they never charge their authors and they all charge about the same commission. But in my experience, there are very few analogues to this in other industries.
So... if you want to be in the business of selling ideas to industry (as opposed to getting that once-in-a-lifetime idea off your chest and cashing out), the thing to do is find an industry, one where you are likely to be trusted, one where you have a sense that they understand how to buy ideas. Invest in that industry, spend time, speak at trade shows, earn your right to credibility. Then, over time, day by day, you'll have the ability to bring them profitable ideas.
Side note: the more complicated your idea is, the better off you are patenting it. Dean Kamen made his fortune patenting wheelchairs and other devices that you and I could never hope to build. On the other hand, if your idea is simple enough to dream up in a week, the only way you're going to protect it is to build it, fast and well.