Speed is the secret of controlling flutter. You didn't say what size bowl you are turning or speed. I turn lamp shades that are usually 15" at the base, 6" at the top and 16" tall. I use a 40 watt bulb shining on the outside to judge the wall thickness which is usually about 1/16". Speed changes of 10 RPM can make very radical changes in the cutting. First turn and finish sand the exterior then start on the interior. Rough turn it to a wall thickness of at least 1/2". Then starting at the rim finish turn the interior in stages of about 1" at a time. As you work toward the bottom and the diameter gets smaller you will need to gradually increase the speed and the finished wall will start to flutter. Once you have finished a section don't try and go back. If you need to clean it up you will have to sand it out. After I finish cut the wall I finish sand the interior at a slower speed supporting the wall on the exterior with my hand.