I have several games on my HD & HD+, with no folders labeled *Burstly, this includes one angry birds app. where exactly in the file structure are the folders labeled *Burstly? It is in the main "data" folder, in the download folder, or in the My Files/My Files subfolder?
The only cache files that show up on my HD are the ones for flixster in the data folder. You probably need to go into Settings/applications/My apps, then check each individual app to see which ones have a cach to clear. Try clearing one at a time, then checking back in your files tofind the guilty culprits.
If you use flixster or vudu, occasionally, when the connectionis not strong, they will cache quite large files, which require clearing.
Don't look "under" MyFiles, select the caret (arrow) to the right. Then you'll see a file structure you're more familiar with (and more functional, much easier to find things.)