Let's examine what a beautiful bourree does: it speeds the dancer across the stage as if she were light as a feather. There is no stop-start, no lifting and dropping. She stays at the same level as she flitters through space.
Multiple exposure of ballerina Alicia Alonso doing bourree, 1944, Life Magazine
New dancers en pointe often have awkward bourrees. They are uneven and, yes, clunky. Here are some simple ways to make yours smoother and more beautiful:
1. Remember the bourree is not a drag but a lift. Each foot lifts off the floor, alternating back-front-back-front, etc. It is not the front leg pulling the back one. Practice this at the barre in place, standing in sousous and holding with two hands. Quickly lift the feet up and down in place and then practice moving along the barre.
2. The ankle must remain straight. If you have a bend at the front of the ankle, you are articulating the wrong part of the foot. Again, practice lifting the toes in the shoes not tapping them.
3. Keep a micro-bend in your knees. If the knees are completely straight, they do not allow smoothness or speed. Neither are the knees completely bent as in fondu.
4. The back foot drives the bourree. A beginning pointe student is likely going to start her bourree from a sousous rather than a pique but in either case, be sure to initiate the movement from the leg that is in back. This will keep the space between the knees small and tight and will avoid the urge to drag.
Final thoughts: Your goal with bourree is to keep the steps small and quick - better to have many small steps than several large ones.You can help yourself (as always) by staying lifted in your torso and lower back. This will (as always) allow more room to move underneath you.
Bonus link! Lisa Howell, of the The Ballet Blog and the creator of the Perfect Pointe system, addresses the issue of hyper flexible feet en pointe in this article. Good stuff!