Can confirm play count, last played date, and date added are stored in your *.mbl library file. If you copy your library folder over to the new install and then open this same *.mbl file in your new install all of your data will be in tact.
It's best if your music files are in the same folder locations on the new install, too. If it's just a name change on the main folder or something uniform, you can get around this with some fiddling, but if you totally rearrange the files outside of MB the program will have a hard time matching your data to your files.
If you use Last.fm, MusicBee can pull your number of plays from there.
This will work for date last played and play count regardless of file location.