The surface tension of water reduces on addition of soap to it. Then why does normal water not form bubbles but soap does even with less surface tension?
To form bubbles, you need less surface tension, not more. Because the surface tension makes bubbles less stable. This is why we add soap.
As a simpler analogy, consider just making a puddle of liquid on a flat surface. If the surface tension is low, you'll have a nice flat puddle. But if the surface tension is high (e.g. with mercury - don't try at home), the puddle will break into smaller puddles or even individual drops of the liquid.
Pretty much the same thing happens to bubbles - the surface tension doesn't hold a bubble together, it tears it apart.