Niobium nanobridge SQUIDs have shown exceptional noise performance with potential applications in quantum information processing, weak signal detection and single spin detection where the nanobridge geometry should enable efficient electromagnetic coupling to implanted spins. Combining such devices with dispersive microwave readout circuitry allows the spin sensitivity to be further improved by overcoming the standard thermal limit. Here we report on the fabrication and dispersive microwave readout of an array of niobium nanobridge rf SQUIDs incorporated into a superconducting resonator, including the optimization of the nanobridge fabrication process by electron beam lithography. We show the measured flux-tuneability of the resonance is in good agreement with theory, and we also discuss how the nonlinearity of the weak-link in the resonator structure allows for the mediation of parametric effects to enhance performance.