The Flight of the Bumble Bee was originally written as a virtuoso piece for the violin, but it's probably been played on every instrument except the harmonica and I wouldn't bet against that either. I've recently taken the opening riff to use as a good cross-picking exercise. I usually play it after I've done some trilling or dexterity exercise, to get my fingers going before a show. It's also fun to whip out in a song every once in a while. It's kind of like when Stevie Wonder plays Mary Had a Little Lamb in Fingertips Part 11.
I play this riff over an Am chord. Lead off with your index finger playing on the 5th fret B string. Then you go down chromatically (fret by fret) on the G string from the 8th fret to the 5th fret.
Now place your middle finger on the 6th fret B string. Follow that note with the first finger on the 5th fret B string. Go on to your pinky, once again on the 8th fret of the G string, followed by yOur index finger back on the B string 5th fret. The final section is a chromatic riff on the G string which again goes from the 8th fret down to the 5th fret, followed by the same notes going back up from the 6th fret to the 8th fret.
If you want to play it as part of a progression, play the riff twice over Am, once over Dm and then back to Am. When the chord switches from Am to Dm, start on the 10th fret of the B string instead of the 5th and play the exact same fingerings as the ones I've just described. So if you want to loosen that picking wrist, get buzzin'.