Trait mindfulness refers to one's disposition or tendency to pay attention to their experiences in the present moment, in a non-judgmental and accepting way. Trait mindfulness has been robustly associated with positive mental health outcomes, but its neural underpinnings are poorly understood. Prior resting-state fMRI studies have associated trait mindfulness with within- and between-network connectivity of the default-mode (DMN), fronto-parietal (FPN), and salience networks. However, it is unclear how generalizable the findings are, how they relate to different components of trait mindfulness, and how other networks and brain areas may be involved. To address these gaps, we conducted the largest resting-state fMRI study of trait mindfulness to-date, consisting of a pre-registered connectome-based predictive modeling analysis in 367 meditation-naïve adults across three samples collected at different sites. In the model-training dataset, we did not find connections that predicted overall trait mindfulness, but we identified neural models of two mindfulness subscales, Acting with Awareness and Non-judging. Models included both positive networks (sets of pairwise connections that positively predicted mindfulness with increasing connectivity) and negative networks, which showed the inverse relationship. The Acting with Awareness and Non-judging positive network models showed distinct network representations involving FPN and DMN, respectively. The negative network models, which overlapped significantly across subscales, involved connections across the whole brain with prominent involvement of somatomotor, visual and DMN networks. Only the negative networks generalized to predict subscale scores out-of-sample, and not across both test datasets. Predictions from both models were also negatively correlated with predictions from a well-established mind-wandering connectome model. We present preliminary neural evidence for a generalizable connectivity models of trait mindfulness based on specific affective and cognitive facets. However, the incomplete generalization of the models across all sites and scanners, limited stability of the models, as well as the substantial overlap between the models, underscores the difficulty of finding robust brain markers of mindfulness facets.