fennel bulb is sprouting -- now what?
Now what? Eat it!
Whether it would survive if you planted it depends on a few things. Are there still roots attached to the bulb? That's the main thing. I don't think you could successfully plant it without the roots. Also, where are you? In most parts of the country, it's getting too warm for fennel. It would bolt (i.e., flower) before very long, at which point the bulb would become too tough to eat.
It sounds like you're trying to get the most out of the bulb by planting it. I think you'd probably get the most out of it by EATING it. As I said above, I think putting it in the ground would either kill it, or cause it to flower almost immediately. In addition, the fact that it's sending up shoots in the fridge means that the foliage is feeding off of the energy stored in the bulb, taking away that sugary goodness that makes fennel so yummy.
So to get the most out of it, put it into your belly. And if you want to grow fennel (again, depending on where you are), buy some seeds and put them in in the late summer or fall. You'll have lots of bulbs and greens to eat come spring.
Hey- give it a try. Dig a hole and put it in there and water. I've had some silly/amazing results that way. The last one was a grocery store sprouting onion that I planted that ended up being something like an Egyptian Walking onion. If nothing else, they say they keep certain bugs away from your garden.
Indeed, if you're not going to eat it, might as well try planting it. Worst case it becomes compost.
Also, even if it does go to flower, the flowers are great attractors for beneficial insects, and taste great too. Fennel pollen is a hot gourmet ingredient these days, you know.
If you've already chucked it but feel like experimenting, try sprouting some fennel seed from your spice cabinet.