I think this should apply for any kind of email, not just for busy people. Actually, this applies to most kinds of writing too.
It'll come off much better if it's well-worded but simple and to-the-point. The more fluffy sentences you add to your email, blog post, internet comment or product copy, the less professional it starts to sound.
I wish I could upvote this more than once. I'm a professional so I don't need requests to be sugar coated. I also don't need lots of detail in the first email. If I'm interested then I will get back to you!