Are there any bulbs that are partial sun to shade.
There are several bulbs which use the 'deciduous' cycle - when trees are bare, they're up and blooming. When the trees are in leaf, they become dormant.
For those that flower in more shaded conditions - bluebells (Hyacinthoides) and Cyclamen (hardy), Oxalis acetosella, some of the fritillaries, Galanthus and, stretching a point because they're not actually bulbs, various Arisaema, Anemone nemorosa.
Think 'dappled' more than deep gloom.
Bound to be lots more but that's a start. ;-).
I just ordered some Seagull daffodils from Old House Gardens and the website reads that they should be protected from full sun for best color. Zone 5-7.
Are you considering spring flowering bulbs (daffs, tulips, hyacinths, etc) or summer blooming things like lilies?
The spring blooming ones do just fine for me in the woods. There are no leaves on when they are emerging and during the bloom cycle. I do think however that they would not do well in permanent shade, like say, in the shade of a building.