Ask Mr. Smarty Plants

First, I think we need to distinguish bulbs from other underground storage structures—corms, rhizomes and tubers.   According to our "Glossary of Botanical Terms", a bulb is:  "A thick, rounded, underground organ consisting of layered, fleshy leaves and membranes."  The fleshy leaves, easily seen in the layers of the onion bulb, store food for the growth of the plant.  A corm, from our Glossary, is: "A short, fleshy underground stem, broader than high, producing stems from the base and leaves and flower stems from the top."  The corm has papery leaves that cover it, but doesn't have the thick layers of fleshy leaves like the bulb.  Rhizomes are thickened horizontal underground stems that allow the plant to spread.  Many lilies have both bulbs and rhizomes.  Tubers are expanded tips of rhizomes, e.g., potatoes.  To add confusion, "bulb" is often used to describe all of the above as well as any other expanded underground part of a plant. 

Flowering plants are divided into two major groups or classes, the monocots and the dicots.  The major recognizable families in the monocots include the lilies, irises, orchids, palms and grasses.  The dicots comprise everything else, e.g., the sunflowers, asters, sages, milkweeds, oaks, elms, etc.  There are many features that botanists use to distinguish between the two groups.  Here are few that are easily seen:  Monocots have flower parts in multiples of three, parallel leaf veins and the feature that gives them their name—an embryo with a single cotyledon.  Dicots have flowers with parts in multiples of four or five, branching or reticulated leaf veins and embryos with two cotyledons.  You can read more about the differences and similarities between the two flowering plant classes from the University of California Museum of Paleontology.

Almost exclusively, species that have bulbs are in the monocots.  Many of the species in the Family Liliaceae (Lily Family) as well as the Family Iridaceae (Iris Family) have bulbs. 

Here are some species in the Lily Family that have bulbs:

• Allium spp., such as Allium acuminatum (Tapertip onion) and Allium canadense (Meadow garlic)
• Calachortus spp., for example, Calochortus elegans (Elegant mariposa lily) and Calochortus macrocarpus (Sagebrush mariposa lily)
• Camassia spp., such as Camassia quamash (Small camas) and Camassia scilloides (Atlantic camas)
• Erythronium spp., such as Erythronium americanum (Yellow trout-lily)
• Fritillaria spp., such as Fritillaria affinis var. affinis (Checker lily) and Fritillaria pudica (Golden bells)
• Hymenocallis spp., such as Hymenocallis caroliniana (Carolina spider-lily) 
• Nothoscordum bivalve (Crow poison)
• Veratrum spp., such as Veratrum viride (Green corn lily)
• Zigadenus spp., such as Zigadenus nuttallii (Death camas)

Here are some species in the Iris Family:

• Alophia drummondii (Propeller flower)
• Nemastylus spp., such as Nemastylis geminiflora (Prairie pleatleaf) 
• Herbertia lahue (Prairie nymph)
• Calydorea coelestina (Bartram's ixia) and here are photos

The Iris spp. themselves, according to the Flora of North America, grow from rhizomes, not from true bulbs.

 You can read more about the Family Liliaceae and Family Iridaceae in the Flora of North America.

There is actually one family of plants in the dicots with some species with true bulbs—the Family Oxalidaceae (Woodsorrel Family).

A paper by K. C. Oberlander et al., "A model of bulb evolution in the eudicot genus Oxalis (Oxalidaceae)" (Molecular Phylogenetics and Evolution Vol. 51 (2009) pp. 54-63) discusses this one dicot family that has bulbs.  A great many species of South African Oxalis have bulbs.  There is one North American native species of Oxalis, Oxalis latifolia (Broadleaf woodsorrel), that has bulbs. 

You might also be interested in reading Bulbs of North America by Jane McGary (2001, Timber Press) and visiting the webpage of Pacific Bulb Society.