The bunnies aren't desperate, just hungry. Lilies store a lot of sweet content in all parts of the plant (which attracts many "critters" to them. Lilies are very hardy, usually no matter what happens to the stem. On a commercial scale, in order to produce larger bulbs quickly, every year for at least two years, I will cut off the stem when they are about four to six inches tall...way before blooming. This forces the plant to put more production into the bulb and will not kill the bulb. So, premature removal of the stem is ok. Placing a fence around the emerging stem is a good idea, but be sure the holes will not allow the rabbits (or any other critter) to enter. Instead, consider using bird netting or other material with small holes. I would not use bone meal in the soil. 1). Lilies prefer acidic soil and bone decreases acidic levels. 2). Bone meal will actually attract more critters and your bulb will more than likely be destroyed. The fertilizer is a good idea, though. However, make sure it is not high in nitrogen (less than 10%) and high in mineral content or you can use a slow release
nitrogen base but make sure it is at least 50% slow release or you will burn the bulb causing it to rot.