Last year, I planted several hundred daffs and hyacinths under a huge Locust tree. I poked holes for the hyacinth bulbs, using a sharpened length of rebar. For the daffs, I carefully dug around the roots, and planted clusters of bulbs, as many as would fit the space, with 4" spacing.

As long as you don't damage big roots, that's 1" diameter and up, you won't hurt the tree. Small feeder roots will grow back with no ill effects to the tree.

I'd think that burying the tree roots in 6" of soil or mulch would do as much harm as damaging the roots.

Something to keep in mind when planting naturalizing bulbs under trees, is the difficulty involved in digging them up to space them out a few years down the road. It'll happen more quickly around roots, because the bulbs and their offspring are in more cramped quarters.

Thanks for the reply, Donn. I think I'm going to abandon the idea - the thought of having to extract the bulbs from a tangle of tree roots in a couple of years when it's time to divide is just too daunting. If something sounds too good to be true it probably is, right? ;-)

Marianne

Well, you probably rightly abandoned idea of planting daffs around dogwood tree, but you still could plant minor bulbs (crocuses, scillas, muscari etc) around it.
All those bulbs should be planted as shallow as 1-2".
You even don't have to dig anything.
Scatter them around, cover with 2" of the dirt and cover by 1" of mulch. Done.
Most of the minor bulbs will naturalize freely and wouldn't need a dividing ever, unless you will want to spread them somewhere else.
2" of extra dirt will not harm existing roots of established tree in any way. The only thing you should avoid is to bury the trunk in a mulch, so start working 1 to 1.5 feet from the trunk and go further out as you wish to.