We define $wt_0$-distance which is a special type of $wt$-distance and obtain some best proximity point theorems involving $b$-simulation functions. Our results are significant, since we replace simulation function with $b$-simulation function, metric space with $b$-metric space, and $w_0$-distance and $wt$-distance with $wt_0$-distance. We also provide some examples to support our results.