1832, "public street carriage," originally a colloquial abbreviation of omnibus (q.v.). The modern English noun is nothing but a Latin dative plural ending. To miss the bus, in the figurative sense of "lose an opportunity," is from 1901, Australian English (OED has a figurative miss the omnibus from 1886). Busman's holiday "leisure time spent doing what one does for a living" (1893) is probably a reference to London bus drivers riding the buses on their days off.
1838, "to travel by omnibus," from bus (n.). Transitive meaning "transport students to integrate schools" is from 1961, American English. Meaning "clear tables in a restaurant" is by 1892, probably from the use of the noun in reference to four-wheeled carts used to carry dishes. Related: Bused; busing.