Most bobbin cases do have 2 screws. One is for the construction of the bobbin case and the one closest to the thread strand that comes out is for adjustment purposes. I have 2 bobbin cases. One I never change and the other I change all the time if working with bobbin work or such as Weezy Rider says.
Think of the bobbin tension and the thread tension as having to adjust how the threads meet. Usually there is plenty of room for adjusting only the top tension. If there isn't then maybe you need to have your machine serviced. Whenever I have had real problems with the upper tension adjustment it was because the machine needed a 'spa day' with my repair person.