Green’s Dictionary of Slang

buggy n.2

[the orig. SE gasoline buggy. The earlier buggy was a light one-horse (sometimes two-horse) vehicle, for one or two people; it is cited as slang in Grose (1785) and Hotten (1859 et al.)]

1. [20C+] (orig. US, also gas buggy) a car.

2. attrib. use of sense 1; thus buggy bandit n., a car thief or one who uses a getaway car after a robbery.

3. [1910s–40s] (US) a wheelbarrow.

In phrases

stay in the buggy (v.) [SE buggy, a coach or carriage/car]

[1920s] (US) to comply with requirements, to act as ordered.