Welcome to the addiction.
The fine dust particles in your bowl appear beause you have tear out in the endgrain. Getting clean smooth cuts across endgrain require very sharp tools. In addition, some woods are more prone to endgrain tear out than others, and cherry is one of those woods that can be a real problem.
You can try several things on your next bowl. One, before you make your final cut, go back to the grinder and return to the bowl with a freshly ground edge.
You can also try using a shear cut, that can be done with a bowl gouge with an Elsworth grind, and the tool held with the flute nearly facing the surface you're cutting. The tool is also held vertical, or with the top of the tool pointing up towards the ceiling, and the bottom, or handle of the tool facing down. With this method you want to take VERY light cuts, because that's what you're doing is shear cutting.
A third method is to use a scraper that you've slightly rounded the edges (to avoid getting a catch) held at an angle so that you're shear cutting with the just the edge.
Another thing to try is to stop the lathe from spinning, and periodically hand sand that area WITH THE GRAIN. Notice in your photo that there are lines that wrap around the bowl, and this can be caused by sanding with the lathe under power, sanding too fast, or with too much speed on your lathe. Many fruit woods, cherry especially can be sensitive to heat when sanding. Trying to sand with too much speed will generate heat buildup and you'll end up burnishing your wood, instead of sanding to remove the tools marks.
I hope this helps. Other things you might try are videos/DVD's, especially to show you the various tool techniques I described above. Even better, if there's a turning club nearby, attend one of their meetings, where you might be able to hook up with a mentor.