Bubbles are round due to a property of liquids called surface tension. This property can be summarized in the following sentences:
“It takes a certain amount of energy (or mechanical work, which is equivalent) to increase the surface area of a liquid. The energy is proportional to the increase in the surface area of the liquid. The constant of proportionality is called coefficient of surface tension and is a characteristic of the given liquid.”
Now, this means that an energetically favorable (a state with the least possible energy) state of the liquid is a state with the least possible surface area. Please note that this is only true in an absence of an external force field (like gravitational). But, the volume of the liquid is constant. It is a known geometric fact that from all the shapes with a given volume, the spherical has the smallest possible area. Hence, bubbles have a spherical shape.