Melt the butter in a small saucepan. Remove 1/4 cup of it and reserve. Add the maple syrup, brown sugar, salt and pepper. Stir to dissolve the sugar. When the sugar has dissolved, remove from the heat and stir in the bourbon. Set aside and keep warm.
Cut the squash into wedges, scooping out the seeds. Place the squash on a rimmed baking sheet and brush with the reserved butter and sprinkle with salt.
Create a cool zone in your grill by banking the coals or turning off one of your burners on your gas grill. Oil the grate and place the squash on the cool side. Cover and grill for 15 minutes. Brush with the bourbon mixture and cover and grill for 5 more minutes. Repeat with the bourbon mixture and grill for 5 more minutes.