The only (scuba) dive experience that I know of at WDW is DiveQuest at Epcot. It's a 45 minute dive in the 6 million gallon aquarium at the Living Seas exhibit. It's a very easy dive, max depth is about 27 feet, all the equipment you need is provided for you (but you can bring your own mask if you wish)
The dive is a lot of fun, and for the money not only do you get your 45 minute dive, you also get to see a video about Disney and environmental preservation, you get a full dive briefing, a backstage tour of the living seas area, a secure locker to use, a changing room with private shower, a t-shirt, soda after the dive, and they do video tape the dive and show it to you afterwards.
I believe it's about $140 for the dive experience, and you can get a 10% discount if your dive certification is from SSI (I believe they may also offer a discount for PADI or NAUI, but I'm not 100% sure on this, as my cert is with SSI)