'bankroller' is formed from the verb 'bankroll' plus the agentive suffix '-er'; 'bankroll' originated in American English in the late 19th century, from 'bank' + 'roll' (a roll of money) meaning to provide funds.

'bankroll' (late 19th c.) developed in U.S. English from the compound of 'bank' and 'roll' referring to a roll of banknotes; the agent noun 'bankroller' then arose as the person who provides a bankroll.

Originally referring to a literal 'roll' of bank money or the act of supplying such funds, it broadened to mean providing financial backing in general; 'bankroller' specifically denotes the provider of that backing.