The story
From Bashi +channel. Bashee, later Bashi, is from a local language term for a type of liquor drunk plentifully by the crew of William Dampier when they landed on an island south of the channel, as reported in Dampier's book the popular sensation A New Voyage Round the World (page 422) published in 1697. According to Dampier, the crew named the island after the liquor. The channel would take the name of the island. (See also basi.)
Etymology from Wiktionary, CC BY-SA 4.0.