What is the best way to get in contact with business experts to give short presentations at my large business conference for entrepreneurs?

I'm going to give you a personal experience.

I wanted some business experts to join a panel of judges and this was my "execution plan":

Research universities and non-profits where this executives or business people give their time.

Why? Most successful people that can teach (both are different skills) feel the need to "give back". So many of them volunteer their time and money on universities or organizations.

If you find those who have this characteristics you will be one feet closer to actually being able to reach them. This is because they are "minded" in helping.

To approach them I will recommend an exchange where they are not benefit of your conference but someone else is. If you tell a company owner that teaches "entrepreneurship" in a university that you want him to give. "Speech or class" and in exchange you will give 10 tickets for his students, he will be much more receptive of the idea.

The other strategy is the one you mentioned and it actually focus on two feelings: possible new clients (leads) form the conference or ego. I would definitely go for the second one, and instead of approaching saying "you will benefit from this" I would go for inflating his/her ego.

Hope this could give you some ideas.

I recommend taking a look through both Pulse and the Groups on LinkedIn. Folks who have great expertise to share are often contributing solid posts. A well-structured and thoughtful post will also show you their communications tone and whether they approach the subject in a way that leaves valuable takeaway thoughts with the reader.

So, my suggestion:

Go to Groups and plug in a keyword for a topic you'd like to find an expert on

Scan for groups with good focus (Technology Entrepreneurs or Integrated Marketing, e.g.) and browse a few of the larger groups discussions. Cjeck the 'popular discussions tab

Engage in the discussion and ask if they would be interested in a speaking opportunity

Repeat for each topic you're seeking expertise.

Hope you find this useful - I have located many subject matter experts throughout the globe this way.

LinkedIn is the best option since your target prospects are likely to be active. But LinkedIn has this problem of not showing you every result, thus becomes a challenge for most.
If you need your target prospects based on different parameters, I can provide the list which should help you.
Let me know if I can be of help.