Hi!
MusicBee already supports fanart.tv for downloading album art (right click in an album art area and choose "Search Internet" or "Search Internet for Picture." I think it only finds cover art, though.
However, since you seem to have yours downloaded already, it's fairly easy to configure MusicBee to show that art. I'm not an expert at this, not having done it this way myself, but I *believe* you would do this:
1. Go into Preferences > Tags (1) (
http://images.wikia.com/musicbee/images/8/85/Preferences_Tags_1.png)
2. Check "link to original picture" (and uncheck embed in file, if you don't want that behavior)
3. Open "set retrieval filter" dialog, uncheck most of them, but check *.* and move it to the top (provided cdart.png is the only artwork in the folder - otherwise I'm not sure how you would point to it specifically). Click Rescan Artwork.
Hopefully someone else can confirm or offer better advice.