Bitter end of the Cable, the End which is wound about the Bitts. ["The News-Readers Pocket-Book: Or, a Military Dictionary," London, 1759]
See bit (n.1). So, when a cable is played out to the bitter end, there is no more left to play. The term began to be used c. 1835 in non-nautical use and with probable influence of bitter (adj.).[bitter end etymology, bitter end origin, 英语词源]