Photonic bound states in the continuum (BICs) provide a standout platform for strong light-matter coupling with transition metal dichalcogenides (TMDCs) but have so far mostly been implemented as traditional all-dielectric metasurfaces with adjacent TMDC layers, incurring limitations related to strain, mode overlap and material integration. Here, we demonstrate intrinsic strong coupling in BIC-driven metasurfaces composed of nanostructured bulk tungsten disulfide (WS2) and exhibiting resonances with sharp, tailored linewidths and selective enhancement of light-matter interactions. Tuning of the BIC resonances across the exciton resonance in bulk WS2 is achieved by varying the metasurface unit cells, enabling strong coupling with an anticrossing pattern and a Rabi splitting of 116 meV. Crucially, the coupling strength itself can be controlled and is shown to be independent of material-intrinsic losses. Our self-hybridized metasurface platform can readily incorporate other TMDCs or excitonic materials to deliver fundamental insights and practical device concepts for polaritonic applications.