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Generating counterfactuals to discover hypothetical predictive scenarios is the de facto standard for explaining machine learning models and their predictions. However, building a counterfactual explainer that is time-efficient, scalable, and model-agnostic, in addition to being compatible with continuous and categorical attributes, remains an open challenge. To complicate matters even more, ensuring that the contrastive instances are optimised for feature sparsity, remain close to the explained instance, and are not drawn from outside of the data manifold, is far from trivial. To address this gap we propose BayCon: a novel counterfactual generator based on probabilistic feature sampling and Bayesian optimisation. Such an approach can combine multiple objectives by employing a surrogate model to guide the counterfactual search. We demonstrate the advantages of our method through a collection of experiments based on six real-life datasets representing three regression tasks and three classification tasks.