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We report on the analysis of ¹⁹F-NMR parameters and complementary magnetic susceptibility in an ambient-pressure annealed powder of LaO_0.5F_0.5BiS₂ with a T_c of about 3K. Measurements were performed as functions of temperature T and applied magnetic field H. The ¹⁹F line position is dominated by the chemical and Knight shifts, which are typically T-independent. Nevertheless, we find a noticeable T-dependence of both the shift and linewidth above 10K and a stronger T-dependence of these parameters with decreasing T below 10K. The bulk magnetization can be fit reasonably well with a modified Brillouin function for dilute magnetic impurities. However, neither the linewidth nor the frequency shift responses to varying T can be attributed to random paramagnetic impurities. This suggests hidden local magnetic degrees of freedom as an alternative source of static fluctuations in the normal state. Ten Kelvin is the maximum T_c this material displays under pressure, or when samples of this material are pressure annealed. The decrease in lineshift, the linewidth increase, and the lineshape symmetry together suggest superconducting fluctuations throughout the sample, and not just in some regions, below 10K. A discussion of spin-lattice relaxation effects is presented to help with characterizing the situation.