The wikipedia article on the strait in English (the Bashi Strait) doesn't say.
The name "Bashi Channel" comes from a kind of sweetcane wine only produced in Batanes. The wine local name in Itbayaten is "Bashi". European sailors had drunk with Bashi during staying in Batanes, and when they passed the channel, wind and current were so strong, just like drinking bashi. So they called the channel Bashi Channel.
Otto's interview with an Ivatan on 2014.05.09