A fun tile behind the floating shelves would look fabulous!

You can do either tile or wallpaper, but since it is a dry bar, I would go with an outstanding wallpaper.

Since you have a dry bar, you could realistically do either a tile backsplash or a wallpaper. You can see below we did a tile in an area where we did a bar for a client.

West Coast Modern on the East Coast · More Info

Wall paper will be easier to deal with for installing the shelving and I would do glass shelves to let the wallpaper show as much as possible also try not to display anything but glass to let the wallpaper shine.