You need one empty space all around the bamboo shoot (the same applies for trees), which ends up making a 3x3 space with the bamboo plant in the middle (you can grow stuff right next to the cobblestone at the train station/plaza/etc., though). I've heard that there are spots where nothing seems to want to grow, though, so you may have just gotten unlucky if you left it enough space to grow. If a sapling (and I'm guessing a bamboo shoot as well) is also surrounded by already-grown trees, they can also die because they're in the shade even if they have the room to grow, so watch for that as well.