I always err on the side of moving my fish to a birthing tank early rather than late. Unlike a breeding trap, a birth tank won't cause the fish too much stress if she is only in it a few days. It really will depend how small the bowl is that you are considering using. If it is too small, it just becomes a breeding trap with a definite disadvantage. It sounds like you probably don't have a filter running on that tank and becoming cycled. If that is the case, get a small air driven sponge filter for the container and get it going by leaving it in the main tank. When the female starts to look quite big, she can be moved, along with the filter, to the birth tank and have a nicely cycled filter for her and eventually for the fry.
For good information on livebearers, I find that tropical fish forums is a pretty good site. I spend much of my on line time there but there are an abundance of livebearer people on that forum.