Why do bubbles form when it rains?
Bubbles consist of a gas trapped by a liquid, where the liquid has a surface tension high enough to encapsulate the gas. This gives bubbles three ingredients: the liquid, the gas, and surface tension. 

The first ingredient, the liquid, is obviously the rainwater.

The second ingredient, the gas, is (also obviously) air. But what isn't obvious is how the gas becomes entrained in the liquid. Asphalt is porous, meaning the microstructure of asphalt consists of lots and lots of tiny random tubes through the solid material. Thanks to the capillary effect, water is sucked into those tiny tubes, and gas is forced out. This gas being forced out of the porous asphalt material and through the liquid on the surface creates bubbles.

Surface tension is the third ingredient, and controls the bubbles' shape, size, and strength. Surface tension can be enhanced by surfactants (big molecules which, when added to a liquid, agglomerate and increase the surface tension). The surface of a road accumulates lots of surfactants - mostly, oil. Oil consists of many long-chain hydrocarbons, which are perfect surfactants (most detergents are actually long-chain hydrocarbons that are polarized at one end). Surfactants tend to agglomerate (that's why, if you pour a little oil on top of water, it will tend to clump together as it spreads out over the surface of the water). Having oil act as a surfactant increases the surface tension of the rain water on the surface of the road, and makes any bubbles formed in the water stronger. That explains the large bubbles you saw.