Current bias evaluation methods rarely engage with communities impacted by AI systems. Inspired by bug bounties, bias bounties have been proposed as a reward-based method that involves communities in AI bias detection by asking users of AI systems to report biases they encounter when interacting with such systems. In the absence of a state-of-the-art review, this survey aimed to identify and analyse existing AI bias bounty programmes and to present academic literature on bias bounties. Google, Google Scholar, PhilPapers, and IEEE Xplore were searched, and five bias bounty programmes, as well as five research publications, were identified. All bias bounties were organised by U.S.-based organisations as time-limited contests, with public participation in four programmes and prize pools ranging from 7,000 to 24,000 USD. The five research publications included a report on the application of bug bounties to algorithmic harms, an article addressing Twitter's bias bounty, a proposal for bias bounties as an institutional mechanism to increase AI scrutiny, a workshop discussing bias bounties from queer perspectives, and an algorithmic framework for bias bounties. We argue that reducing the technical requirements to enter bounty programmes is important to include those without coding experience. Given the limited adoption of bias bounties, future efforts should explore the transferability of the best practices from bug bounties and examine how such programmes can be designed to be sensitive to underrepresented groups while lowering adoption barriers for organisations.