S/E Michigan Zone 6ish

S/E Michigan Zone 6ish

I have a question about adding compost to an already established garden. I want to add it because I know it is beneficial and I don't want to fertilize etc., but I don't want to uproot anything or unearth any bulbs. I added peat moss 2 years ago when I first began my garden, but I unearthed a bunch of daffodil bulbs and now not only do they not flower, but they are haphazardly placed all around. How can I add compost without digging, rototilling, etc.? Can I use a hand rake? Just put some on top and cover with mulch? What do you suggest? How much (as in thickness of inches) should I add approximately? Also, will the daffodils "recover" and bloom again? PS: I already have a thin layer of mulch down from last year.
My room.

My room.

Two firsts :D

Two firsts :D

IDs, please

IDs, please

Daylily Dilemma

Daylily Dilemma

buds and seeds

buds and seeds

raised bed materials

raised bed materials