finally something I am good at!
First off, regard anything said in this post with great caution until vetted by more experienced turners. What I am very very good at is destroying bowl rims starting inside cuts!
The first thing to address is the twist of the bowl gouge in your hand, the angle of attack of the cutting edge. The top edges of the flute when it is laying on the tool rest, the C should be just like the C in my message with the open part of the C facing the bottom of the bowl. Then open the C only a few degrees, have the top of the C the tiniest bit behind the bottom of the C so the cut starts with the bottom of the gouge. Even when cutting aggressively deeper in the bowl the flute should never be laid over past 45 degrees and half that is plenty for those of us just trying to get a finished bowl produced.
Now what I haven't seen is any talk about the bevel of your gouge and it is critical. For the final starting cut the bevel on the nose of your flute should be exactly parallel to the outside wall of your bowl so you are making a cut parallel to the outside. However, an often used cheat is to pull the handle further towards you and make a very shallow angle cut towards the inside of the hollowed part of the bowl. Do this several times just making a tiny nick on the inside of the bowl rim, gradually working towards the parallel angle you are seeking.
SMALL CUTS, carefully supported with the tool rest close are the secret to starting an inside cut. Too aggressive, wrong angles, BLAM! Also, a tip from metal working that is more conservative than wood turners usually practice, especially good ones, never take more than one-third of your remaining material off with one pass. It is possible to take more but one third is very conservative and will help keep a beginner out of trouble. A highly experienced turner will turn a bowl in a tiny fraction of the time a beginner can. Speed ain't our game right now, getting to that sanding and finishing stage is!
I haven't looked for awhile but go to youtube and search on Lyle Jamieson. A master with the gift of explaining things to beginners and the clearest and best free video's I have found. "Free" is relative, I will be buying his DVD's and some of his tooling, exactly what the free video's are intended to do. However there is a tremendous amount of great information in his free videos. Have to admit that with my horrible internet speed here and bandwidth limitations I downloaded the video's to watch. If you can't watch them on youtube, PM me your e-mail and I'll send you the most relevant. There should be around twenty of his videos on youtube and I consider them all gold!
Finally tip, sharpen your gouge before starting to try to create a rim, and sharpen again every few passes. A sharp gouge makes things far easier, scary sharp is best. The gouge should go through the wood almost by itself. If you are having to force it with more than gentle pressure something is wrong, stop and figure out what.
Just a fellow beginner and bowl buster,
Hu