Cognition underlies animal behaviour, which is key to successful conservation strategies, yet largely under-utilised in conservation, though there are recent calls for closer integration. Conservation-relevant cognitive abilities can impact on adaptability and survival, such as neophobia, e.g., responses to novelty, and innovation e.g., problem-solving, particularly in today’s changing world. Bali myna are a critically endangered endemic species, which are a focus of active conservation efforts, including reintroductions. Therefore, gathering cognitive data can aid in improving and developing conservation strategies, like pre-release training and individual selection for release. In 22 captive Bali myna, we tested neophobia (novel object, novel food, control conditions), innovation (bark, cup, lid conditions) and individual repeatability. We found effects of condition and social environment, including longer latencies to touch familiar food in presence than absence of novel items, and between problem-solving tasks, as well as in the presence of conspecifics, compared with being alone, or with conspecifics and competing heterospecifics. Individuals were repeatable in latency responses: 1) temporally in both experiments; 2) contextually in innovation experiment and between both experiments (and approach order), suggesting a stable behaviour trait. These findings are an important starting point for improving conservation strategies in Bali myna and other similarly threatened species.