"unicellular microorganisms which lack an organized nucleus," and sometimes cause disease, 1847, plural of Modern Latin bacterium, from Greek bakterion "small staff," diminutive of baktron "stick, rod, staff, cudgel." So called because the first ones observed were rod-shaped. Introduced as a scientific word 1838 by German naturalist Christian Gottfried Ehrenberg. A classical plural sometimes also erroneously used as a singular.
The Greek word is from a PIE *bak- "staff used for support, peg" (compare Latin baculum "rod, walking stick;" Irish bacc, Welsh bach "hook, crooked staff;" Middle Dutch pegel "peg, pin, bolt"). De Vaan writes, "Since *b was very rare in PIE, and Celtic shows an unexplained geminate, we are probably dealing with a loanword from an unidentified source."
word-forming element indicating "branch of knowledge, science," now the usual form of -logy. Originally used c. 1800 in nonce formations (commonsensology, etc.), it gained legitimacy by influence of the proper formation in geology, mythology, etc., where the -o- is a stem vowel in the previous element.
The second element is prop[erly] -logy (-logue, etc.), the -o- belonging to the preceding element; but the accent makes the apparent element in E[nglish] to be -ology, which is hence often used as an independent word. [Century Dictionary]
<a href="https://www.etymonline.com/word/bacteriology">Etymology of bacteriology by etymonline</a>
Harper, D. (n.d.). Etymology of bacteriology. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/bacteriology