I think the airlines decide when to offer a bonus.
Not quite. Either an airline may lower price per unit for a certain period (often done as a rebate to a merchant), or a bank may choose to temporarily reevaluate their performance obligation to customers. Normally airline and bank would agree to split costs of a promotion. Airline benefits by improving cashflow, while bank recognizes deferred revenue (I think starting last year GAAP no longer allows accruing costs with imididiate revenue recognition). Interestingly, with this new accounting rule banks now have little incentive to do promotions, since they will always negatively impact their revenue, so it is almost always an airline.