To make a bee-line is to follow the example of bees int taking the shortest route from one place to another. The expression comes from the belief that bees return to the hive by the shortest possible way after they have gathered their food. And the shortest distance between two points is, of course, a straight line.
But on their return home, the bees sometimes make lines which are far from straight. These are dancing movements in the air to inform other members of the colony about their source of supply. They indicate whether the food is pollen or nectar, the direction and distance from the hive and even the colors of the flowers.
This bee code was discovered by the German naturalist Professor K. von Frisch. He found, for example, that a circular dance says the food source is close to the hive and that a waggle dance indicates long distances.