Are you looking for spring or summer flowering bulbs? Some spring flowering bulbs that come to mind are chionodoxia, scilla siberica, grape hyacinth, pushkinia, crocus. These are all small but very pretty. Botanical tulips are also quite attractive and very different from regular tulips in that they are small and very hardy. My favorite is tulip tarda.

It's the evergreen trees that bother me... So many of them are quite shallow-rooted and 'hungry'. I can think of many of my own NZ natives that fall into this category. As you already know, the ivy will cope just fine because of its rooting system. Before you spend on woodland bulbs - check what's under the soil. And - be prepared to add plenty of good and ancient leaf mould/compost because your soil will probably be short on humus. It could also be a chore to dig. You may be able to use some form of hugelkultur to offset the drawbacks for a few years as you say your lot has not been built on. If you also have deciduous trees - hardy Cyclamen are glorious under maples. Chionodoxa will be fine and also grow in company with Hosta (but deer are very partial to those...) Not quite bulbs - the woodland Anemones, and Sanguinaria. Also Epimedium. The new growth can be lovely in spring. If you have rich patches - light wells and good soil - patches of the smaller Liliums - mackliniae is a pleasant pink, for example. I'd agree on the fritillaries and would be more inclined toward pontica. It can go 'rice grain' if not planted deeply enough - but many are like that. You could try with Narcissus - some of the species and crosses from cyclamineus do quite well in a deciduous tree environment with shade thereafter. I'd also agree on the Arisaema and Arisarum. The leaves alone can be very pleasant. However, they, too, have rule the world tendencies. Not in the least bulbous: Chiastophyllum, Brunnera, Helleborus and Corydalis - but they can be very shade and drought tolerant once they've settled in.

I want to know too! Fwiw, before Google, a botanist at Pearl City at extension service told me it was gumi or goumi, a Japanese ornamental. Now that I search on that name, gumi looks nothing like this plant. Good thing I cut it down and yanked the root from my garden back then!

Almost certainly Galium aparine, aka cleavers or bedstraw. It pulls out easily in moist soil but also breaks off easily. My pup is forever bringing in pieces of it attached to his fur after doing his rounds of the exterior of the garden where it abuts the greenbelt.