Paint for stencils on black fabric
Your problem is the opacity of most fabric paints; most liquid ones are only designed to work effectively on a white or light-colored shirt, and the thick plasticky &quot;puffy paint&quot; writers aren't going to be effective over large areas or in stencils.
If you're working with just white, opaque white screen printing ink for fabric works very well. It will handle similarly to paint, and like paint you'll need to be careful about it bleeding over the edges, but it will bind to the fabric and retain its white color. Unfortunately, most other colors of screen printing ink tend to be translucent, with the expectation that they would be applied over a layer of the white ink. While aligning the two layers is fairly trivial in a professional setting, it may be more challenging with a hobbyist setup using regular stencils. As you mention just &quot;solid bright white&quot; in your question, however, this is likely your best bet.
Screen printing ink can be purchased in most places that sell art supplies, as well as some crafting supply stores; be sure to check that the type you are purchasing is for use on fabric (Speedball brand has distinct formulae for paper vs fabric printing, while Jacquard branded inks are formulated for both grounds; other brands may vary). Follow the instructions for setting as described on the container for your best results.