Solving inverse problems is computationally expensive, if not infeasible, under specific scenarios. For example, many forward solutions are required when solving inverse problems using Bayesian techniques. In this work, a novel inference protocol is established, that can be used to infer the cardiac bidomain conductivities and the cardiac fibre rotation angle (bidomain parameters). This protocol uses a surrogate model, developed using generalised polynomial chaos techniques, to approximate cardiac potentials on a multi-electrode array. The resulting surrogate model is used in conjunction with Bayesian inference techniques to infer the bidomain parameters. A lower-order surrogate model (order three) can effectively characterise the influence of the extracellular conductivities and fibre rotation on the cardiac potentials; however, it is recommended that a higher-order surrogate model expansion of order seven be used to adequately characterise the influence of the intracellular conductivities as well. This seventh order surrogate model was successfully used to infer the extracellular conductivities and fibre rotation angle from a single set of synthetically generated noisy experimental potentials, while the intracellular conductivities were unable to be retrieved accurately under this scenario.