I use wooden stakes driven in at a slight angle and then lean the tombstone against that as I push the little metal stakes into the ground. So the stake is supporting the backside of the stone, and it leans into the stake slightly - most side/front wind won't budge them that way, it would only be strong winds from the backside that would dislodge the stones then. This setup works for me most of the time.
I would also suggest trying to put the bamboo into the ground first (not a whole length - say cut them down to be around 10 inches total), then sliding the stones onto the bamboo (make sure there is at least 4-6 inches above ground) but again this isn't a perfect fix, and you should also probably use an electric drill to create the holes in the bottom of your stones so you don't rip them up trying to push in the bamboo.
Most folks use short lengths of pvc tubing glued to the backside of their stones (liquid nails works well) and then drive rebar into the ground and slide the pvc collars over that. OR you could build a small base out of plywood or even more foam, attach your existing stones to those as a wider base can be secured much easier than the standalone stones.
I'm fine with the wooden stake/flimsy metal stakes that comes with them since I have my fencing enclosing all of my graveyard - it also corrals the stones if they decide to fly off.