Given the shortfall in students studying science, promotion of motivation and engagement in science education is a priority. The current study applied the trans-contextual model to study the motivational predictors of participation in science learning activities in secondary-school students. In a three-wave design, secondary-school students completed measures of perceived autonomy support, autonomous and controlled motivation, social-cognitive beliefs (attitudes, subjective norms, perceived control), intentions, and self-reported participation in out-of-school science learning activities. Five-weeks later, students self-reported their science learning activities. Students' science grades over the semester period were obtained. Bayesian path analyses supported model hypotheses: in-school autonomous motivation predicted out-of-school autonomous motivation, beliefs, intentions, science activity participation, and science grades. Specifying informative priors for key model relations using Bayesian analysis yielded greater precision in estimates. Findings provide evidence for a link between students' autonomous motivation toward science activities across contexts and may inform interventions promoting motivation and participation in science activities.