Bicarbonate, originally known as bi-carbonate of potash, was coined by William Hyde Wollaston in 1814 based on hydrocarbonate's potential to release two molar equivalents of carbon dioxide (referred to as carbonic acid at the time) as released by both potassium hydrocarbonate (initially known as carbonate of potash, suggested to become bicarbonate) and potassium carbonate (vaguely known as subcarbonate, suggested to become carbonate) upon formation of potash (potassium oxide).
Bicarbonates have historically been defined as, "combinations of the bases with the carbonic acid, in which two atoms of the latter are united to one of the former" In other words, potash (potassium oxide) was well-understood to be a caustic base and essentially the core molecule that subsequent chemical nomenclature was built upon. Carbonate of potash (potassium carbonate) must contain a carbonic acid species fixated within potashs alternative composition (see fixed air above). Since "bi-carbonate of potash" liberates a double dose of carbonic acid, to distinguish between the similar substances, the prefix bi- indicates the bi-carbonate of potash (potassium hydrocarbonate) contains twice as much  fixated in this form potashs composition relative to the carbonate of potash. The same ancient logic (prior to the understanding of molecular formulas and reaction stoichiometry) applied to soda, carbonate of soda, and bicarbonate of soda.
The word saleratus, from Latin sal æratus (meaning "aerated salt"), was widely used beginning in the 1840s.