Exclusion of light works. The most effective way to do this is to cover the ground with carpet, cardboard, layers of newspaper, etc.

I assume you actually mean bindweed, and not the traditional morning glory. As long as you don't intend to plant any seeds in your flower bed, just use Preen(R) according to directions. It's the leftover bindweed seeds that keep coming back. Preen will prevent them (and all other seeds) from sprouting.