The prevalent take-make-consume-dispose behavior for plastic products has raised serious environmental problems stemming from their non-degradable and never-ending life cycle. To address this pressing issue, a few successful attempts have been made to design recycled composite polymers through the traditional trial-and-error design procedure . However, it comes aas no surprise that machine learning is nowadays able to guide the design process in a more effective manner. Despite the recent advances, standard machine learning approaches still struggle to learn material constitutive laws for recycled composite polymers. In addition to the challenges already posed by the modeling of neat composites, the recycling process brings further complexity to the table. Moreover, quantifying the inherent uncertainty of such materials mechanical response is of the utmost importance for their adoption in real applications. In this contribution, Bayesian deep learning is leveraged to learn the material laws of recycled composite polymers. This approach is motivated by its natural handling of noisy data and its embedded uncertainty quantification. First, a representative dataset is computationally generated to capture different sources of uncertainty involved in the recycling process. Then, different state-of-the-art Bayesian deep learning approaches are discussed and the Stochastic Gradient Langevin Dynamics (SGLD) method is adopted to learn the composite behavior. Several results demonstrate a promising performance of such an approach to predict the material constitutive law and to quantify the associated uncertainty. This opens new avenues to design and optimize better sustainable composite polymers with a robust and predictable behavior.