No, you can only bombard cities, and only when that city is above 0% defense. Which is ok, all bombarding does is reduce a cities defense anyways (maybe forts too, but never actually been in a position where I needed to kill one).
If you want to destroy an improvement on a tile, you can just ransack it while standing on it with a military unit (believe all military units have this option aside bombers and fighters).
If your looking to deal collateral damage to a stack, you need to attack the tile with the artillary. You may lose the artillary doing this, but you deal a decent amount of damage to many/all units on the tile.