Atomically thin transition metal dichalcogenides (TMDs) possess a number of properties that make them attractive for realizing room-temperature polariton devices(1). An ideal platform for manipulating polariton fluids within monolayer TMDs is that of Bloch surface waves, which confine the electric field to a small volume near the surface of a dielectric mirrors(2-4). Here we demonstrate that monolayer tungsten disulfide can sustain Bloch surface wave polaritons (BSWPs) with a Rabi splitting of 43 meV and propagation lengths reaching 33 mu m. In addition, we show strong polariton-polariton nonlinearities within BSWPs, which manifest themselves as a reversible blueshift of the lower polariton resonance. Such nonlinearities are at the heart of polariton devicess(5-11) and have not yet been demonstrated in TMD polaritons. As a proof of concept, we use the nonlinearity to implement a nonlinear polariton source. Our results demonstrate that BSWPs using TMDs can support long-range propagation combined with strong nonlinearities, enabling potential applications in integrated optical processing and polaritonic circuits.