Remove drawers from bureau, and apply painters' tape to edges or any area you don't want painted. (If the drawers have pulls attached, unscrew them and set them aside.)
Mist 1 side of the caning with spray adhesive, and stick it to a drawer front.
Position the drawer so its front is completely flat and faces up. Holding spray-paint can about 1 foot above the drawer's surface, and moving steadily from side to side, coat the front. Let dry a few minutes, and remove caning.
Adhere caning to the next drawer, and repeat step 3. You can use the same piece of caning 3 or 4 times. (You will not need to spray on additional adhesive.)
Bureau Blue painters' tape
Sheet of caning, cut to fit the drawer front, 3/4-inch mesh, 18-inch width, caning.com
Enamel spray paint
And the easiest way to transfer the pattern to furniture, such as this dresser, is to use caning sheets as stencils.