I'm no expert, but it sounds like you're either a) heating one side of your bead more than the other or b) holding your mandrel at a slight angle. If you do this, the side you're holding down (or the side you're getting hotter) will have a pucker while the other side gets all pointy.
Heat will pull the glass toward one side or the other - when that happens, the glass puckers around the mandrel in the direction it's being pulled, but the far side loses glass and you get the sharp point on that side. Same thing if your mandrel is tipped even a little - the down side will have a pucker, while the up side has a point.
Ideally, you want to start with the smallest possible footprint (the initial round of glass laid on the mandrel) and build up from there. I use
Jim Smircich's technique to make nice round beads (which I don't make many of, since I'm mostly into smashed organics these days). It's a little slow at first, but you'll quickly get a handle on how the glass flows and forms those puckers.
Hope that helps -