There are many ways to tackle the bumps. The general rule of thumb is that learning to pick your line is the key ingredient to navigating these things. I have discovered that my prefered method is to traverse each bump about midway and ride around them. When I have picked a spot to make a turn, I generally fully flex as I approach the spot, then while banking off the mogul in front of me, I rapidly extend, unweighting my board and then spinning downhill to plant the board in the trough headed the opposite direction. As you are riding across the bumps, it is crucial to remain loose and allow independent flexion and extension of the legs in order to maintain a quiet upper body while allowing the board to ride up and over the bumps. Going slow is the key to learning to ride these things and it is more than acceptable to come to stop at the point you are going to do a pivot turn or "Leaper" to ride back the other direction. As you become better, you will be able to maintain a realatively constant speed and turn shape as you ride through a mogul field.
Riding through these is a great workout for the core muscles and abs. If you are ever freezing your butt off on the hill, go find a good mogul run to hit and you will no longer be cold. In this video, I demonstrate my technique of doing this.
Snowboard Intermediate Lesson: riding Moguls