Hi there,
it depends. In order to thrive in the long run, spring bulbs need full sun while flowering and some time after that, in order to store enough energy.

so, early flowering bulbs and late leafing out trees should do fine.
Another aspect is soil moisture. Most of the tulips and ornamental leek come from semi-desert like places or steppes.
That means, moisture after winter when snow is melting, and a hot dry summer, with dry soil.

and mind root competition. Is the area just shaded by a tree or do you want to plant within a dripline of a canopy?

Stuff like Scilla siberica do well around trees as they are a woodland species,
I would be careful with tulip hybrids and Crocuses.

Well then, have a go at it anyway,

bye, Lin

Thanks for the advice, Lin.

I googled Scilla siberica and about lost my breath. STUNNING. I have to get me some of that!

I've got a long narrow bed against the house in the back yard (I'm moving next week to this house). The house isn't straight, so this bed runs from southwest to southeast.

I wasn't planning on the bulbs there because I don't think it gets ANY sun (still have to study sunlight once I'm moved in). There's an overhang. Right now it's just WHITE ROCK. LOL.

Previous owners planted lots of white landscaping rock, but nothing else.

So I'm thinking in that space, definitely some woodland plants: Lily of the Valley (my favorite), now this Scilla siberica, some sweet william and a few other things that grow in the woods natively. Sure miss living in the woods where I could just go dig these things up!

Also I guess some hostas and astilbe, and see how those do.

I'm not really sure what else to do with it.

If you're going to get squill, Brent and Becky's had an extra-large variety in this year's catalogue that I thought looked like an improvement on the standard tiny ones I have: https://store.brentandbeckysbulbs.com/spring/productview/?sku=38-0108
They also have a white variety:
https://store.brentandbeckysbulbs.com/spring/productview/?sku=38-0107

One bulb that I know will not work in the situation you describe is dutch iris; I have some that are shaded by my grapevine once it leafs out and they have never bloomed there. :/

Winter aconite (Eranthis hyemalis), squill, chionodoxa, snowdrops (Galanthus), puschkinia, Anemone nemorosa (you might have to buy this one as potted starts), hepatica (also potted), Corydalis solida and erythroniums will all do well in the conditions you describe.

Sun and Ispahan, thank you! I really love these.

Since they mostly seem to bloom early spring, would you wait until fall to plant the bulbs?