1909, "person who plays the double-bass" (earlier in German), from bass (n.2) + -ist. By 1958 as "person who plays the bass electric guitar."
Entries linking to bassist
bass n.2
"lowest part of a harmonized musical composition," c.1500, from bass (adj.) or the cognate noun in Italian. The meaning "singer having a bass voice" is from 1590s. The meaning "bass-viol" is from 1702; that of "double-bass" is from 1927.
-ist
word-forming element meaning "one who does or makes," also used to indicate adherence to a certain doctrine or custom, from French -iste and directly from Latin -ista (source also of Spanish, Portuguese, Italian -ista), from Greek agent-noun ending -istes, which is from -is-, ending of the stem of verbs in -izein, + agential suffix -tes.
Variant -ister (as in chorister, barrister) is from Old French -istre, on false analogy of ministre. Variant -ista is from Spanish, popularized in American English 1970s by names of Latin-American revolutionary movements.