Disney is no worse with bedbugs than anyplace else. Bedbugs are a new trial for American travelers so they get a lot of press, but they aren't THAT common. It's just that, whenever it happens, people get excited and run around yelling about it, y'know? Anywhere there are a lot of people, particularly a lot of international travelers, there's some risk, but I doubt it's any worse at Disney than at any other place in Orlando.
Follow the basic advice you'll find anywhere - keep your luggage on luggage racks or hard surfaces; don't drop your laundry on the floor; don't take your own pillow or keep it covered if you do, etc. If you are really worried about it, you can inspect your room when you get there - take a flashlight and (if you'd like) a magnifying glass. Check along the mattress edges and the headboard. This site will give you some hints what to look for, but is not for the faint hearted. :p:
http://extension.entm.purdue.edu/public ... edbug.html
Remember that public health employees tend to get more wound up about things than strictly necessary - they get a skewed view of reality because they see ALL the local cases, and don't see the many, many more people who don't have any problems at all. Being careful and checking everything is fine, but if you just want to not worry about it, the odds are still way against you having any problems. :)