I second Al's comments, and agree you need to be fastidious about Anchor, Bevel, then Cut. As everybody knows, but you asked for a reminder: to make a bead, you start with the flute up (open), to one side of the center of your bead, resting on the wood without cutting. Then raise your right hand until the edge starts to cut, and roll the tool as you continue to raise, until the flute is fully horizontal (closed). If you need a bead that is wider than the natural size of your gouge, you will also need to slide sideways. The relative rate of raise-roll-slide determines the shape of the bead. (I never start making a bead with the gouge fully open--it's always rolled a little in the direction I'm going.)
Asymmetry is normal when turning beads and you have to work at it to get symmetrical ones. One 'trick' that helps me is this: when we grab the gouge in a handshake fashion, the gouge is comfortable to hold and apply to the wood. HOWEVER, our wrist naturally rolls easier and more fully counter-clockwise (anti-clockwise for Brits) than in the opposite direction, contributing to the asymmetry. Therefore, when we roll a bead, we should hold the gouge in the finished position, then grasp it. The starting position will be a little tight and uncomfortable, but it will get easier and more comfortable as we roll the bead and the bead will be more symmetrical.
Another tip is that you can always use very, very light cuts to refine the shape of your bead. If it's not perfect with one pass, make a few more careful, light passes. Be aware that doing so can affect the spacing to the adjacent feature.
