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Graph-guided semi-supervised learning (SSL) and inference has emerged as an attractive research field thanks to its documented impact in a gamut of application domains, including transportation and power networks, biological, social, environmental, and financial ones. Distinct from SSL approaches that yield point estimates of the variables to be inferred, the present work puts forth a Bayesian interval learning framework that utilizes Gaussian processes (GPs) to allow for uncertainty quantification – a key component in safety-critical applications. An ensemble (E) of GPs is employed to offer an expressive model of the learning function that is updated incrementally as nodal observations become available – what caters also for delay-sensitive settings. For the first time in graph-guided SSL and inference, egonet features per node are utilized as input to the EGP learning function to account for higher order interactions than the one-hop connectivity of each node. Further enhancing these attributes through random features that encrypt sensitive information per node offers scalability and privacy for the EGP-based learning approach. Numerical tests on real and synthetic datasets corroborate the effectiveness of the novel method.