Make a bee-line for
Go directly towards.
The phrase derives from the behaviour of bees. When a forager bee finds a source of nectar it returns to the hive and communicates its location to the other bees, using a display called the Waggle Dance. The other bees are then able to fly directly to the source of the nectar, that is, 'make a beeline' for it. This dance is a surprisingly sophisticated means of communication for a creature with such a small brain. The forager bee performs a short wiggling run - hence the name, with the angle denoting the direction of the nectar-laden flowers and the length of time denoting the distance.
The phrase is American and all the early citations of it come from the USA. The earliest that I can find is from The Davenport Daily Leader, January 1808:
"Gustav Stengel Sr., of Rock Island, was thrown from his sleigh on Third Avenue in that city yesterday afternoon, the horse becoming frightened and turning abruptly, ripping the cutter. The horse made a bee line for home."
Given the colloquial usage in that citation, the figurative phrase and certainly the original literal meaning of bee-line must have been in use for some time at that date.
See also: as the crow flies.
See other phrases that were coined in the USA.