I definitely would NOT send a letter and hope for the best. Companies usually will not accept "blind" submissions, as this can open them up to lawsuits. And a lot of what is conceived is done "in-house" - they do not look to freelancers for ideas. However, if you have a great idea, you should submit it. First, though, you need to protect your idea.
There are several ways you can go about protecting your idea. First of all, you are right that a copyright cannot protect an idea - however, a copyright CAN protect any original expression, including detailed outlines, plots, characters, themes, dialogue, sequence of events and so on. Copyrights can cover detailed outlines. You can copyright any of these if they are distinctive and well developed.
Your idea should be fleshed out from the basic idea to a full outline, with details, well-developed characters, some dialogue. You can then register this with the U.S. Copyright Office. You can also register your idea with the Writers Guild of America. This, however, only provides an additional legal record of your idea and does not take the place of a registered copyright.
After protecting your idea, you can approach studios with your concept, but do not submit ideas if they do not agree that use of your concept is conditioned on payment. Having a non-disclosure agreement signed is a good idea as it gives you a contract that can be enforced.
If you get an appointment, have a "logline" or basic idea available (30 words or less) and leave behind a written version of your "pitch" for the tv show. You should have a bare bones outline, and a full outline available (the full outline should have some character development and some dialogue). Mark everything with your copyright, name and date of copyright.
Watch for additional posts from others on this forum who may have better or different advice.
