Paul, a good general book is "Growing Bulbs" by Martyn Rix. it contains the basics of every kind of information on how bulbs are structured and grow in different parts of the world, as well as cultivation recommendations. It can often be found used -- try Amazon and Powell's. The first thing to know is the difference between a true bulb and a corm. Tulips (true bulbs) do not naturally act as you describe. Normally the main bulb persists, unless it has been planted too shallowly, in which case it may produce a "dropper" to get deeper into the soil. I have 10-year-old species tulips still flowering without having increased vegetatively; these probably reproduce in nature mainly by seed.