'bankroll' originates from English compound formation (late 19th century), combining 'bank' and 'roll'; 'bank' comes from Old Italian 'banco' meaning 'bench, table' (used by moneylenders), and 'roll' from Old French 'rolle' (from Latin 'rotulus') meaning 'a roll (of paper)'.

'bankroll' originally referred to a roll of banknotes or a supply of ready money; by the late 19th century the noun 'bankroll' (a roll or supply of money) was established in American English and the verb 'to bankroll' (to provide funds) developed from that noun.

Initially it meant 'a roll of banknotes' or 'ready cash', but over time it evolved to mean 'a supply of money' generally and then the action 'to provide money for' (the verb).