Green’s Dictionary of Slang

(US campus) to get a tan in a tanning booth.

1989		P. Munro Sl. U.
1996		Eble Sl. and Sociability 41: Examples of rhyme from college slang are [...] fake and bake ‘get a tan in a tanning booth’. [Ibid.] 71: Fake bake ‘get a tan in a tanning salon’.
1997–2002		Hope College ‘Dict. of New Terms’ 🌐 fakebake v. intrans. To tan in a tanning bed. [...] ‘If you fakebake too often, you’re going to end up with skin like leather.’.