You may want to look at some of the Marriott Vacation Club Options in the area. One of my favorites is the Marriott Grande Vista that features single rooms, one bedroom and two bedroom villas fully equipped. There are several pools, restaurants, golf, and other daily activities available. This location is close to Sea World and Universal Studios. Disney is about 5 miles away.
If you need to be closer to Disney there are several other smaller Vacation Club properties that are less than 2 miles from Disney including Imperial Palm Villas, Sabal Palms, & Royal Palms.
Would you consider a nice RI, that you make arrangements with to insure you are in an "Adult wing" for privacy? A lot of adults like the RI for their comfort and flexibility.
It would be worth a call to one of your choice!
Good luck, I just don't know of a property in Orlando that caters to "Just adults"!