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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?

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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.

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