I don't have bulb beds. All the bulbs are in mixed beds with perennials and shrubs. They all get mulched with compost.

In late fall I put both compost and shredded pine bark mulch on all beds, including the areas with bulbs. In spring I usually remove mulch from the bulb areas though I might not do it any more because all bulbs, including early tiny ones (winter aconite, snowdrops, iris reticulata, and such), seem to do fine growing through the mulch. I noticed it whenever I would be running late removing it. The mulch I use does decompose so the thickness is not the same as when put in the fall. I think the bulbs appreciate it in winter and it helps improve the soil, so I think it's a win-win situation with organic mulching.

I second the comment above. If you don't mulch, the weeds will take over.

Only with leaves...but I have a lot of them.