Iris and tulips would be bulbs that flower immediately after daffodils.
snow drops, crocus, winter aconite come first in late winter
early tulips, giant crocus, anemone, narcissus, and hyacinth bloom in early spring
then come grape hyacinth, later daffodils, mid-season tulips
in late spring are late tulips, english blue bells, wood hyacinth, golden bells daffodil
end of spring, beginning of summer brings iris, asiatic lilies, hardy glads
mid summer is regular lilies, gladioli, dahlias, late iris varieties
this is of course not an exhaustive list.
Note that if you love daffodils or tulips (for example), you can prolong the bloom season of your favorite flower, by buying early, mid, and late varieties.