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We implement an experimental approach to directly measure the lifetime of guided polaritons arising from the strong-coupling of GaN excitons and the guided photonic modes of a slab waveguide. Using a Fourier imaging setup, combined with spatial filtering of the emission, the emission associated to polaritonic modes with well-defined propagation constants can be selectively analyzed in the temporal domain. By directing it to the entrance slit of a streak camera, time-resolved photoluminescence (TRPL) measurements along the polariton dispersion branch were performed at 40 K, enabling to assess the time decay of polariton modes. By combining this information with the photonic/excitonic fraction corresponding to each polariton mode, extracted from a coupled-oscillators model that indicate a Rabi splitting of $\mathrm{\ensuremath{\Omega}}=80\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, we could extract the photon lifetime in the waveguide ${\ensuremath{\tau}}_{\ensuremath{\gamma}}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}3\ifmmode\pm\else\textpm\fi{}1$ ps. This corresponds to a record $Q$-factor in the UV of 16 000. The excitonic reservoir lifetime, which contributes to polariton formation, was determined through TRPL measurements on excitonic luminescence. Finally, measurements conducted at lower temperature highlight secondary feeding mechanisms for the guided polaritonic mode, either via photon recycling from the AlGaN cladding layer or through resonant injection of photons from transitions below the band gap.