As long as the underlying soil drains properly, mulch and surface moisture retention shouldn't be an issue. I live in an area that typically has very damp soils in winter (our primary rainy season) yet bulbs grow very well here, provided the underlying drainage is good.

Got it. So the concern is mainly as long as they are not waterlogged.

But the soil being moist due to mulch on top is not a major or majorly concern.....Heh, I was just thinking in my mind, bulbs, nice dry soil, not even damp to feel was the primary goal. I guess building bubble house around the soil beds is not always a easy option ;-)

"nice dry soil, not even damp to feel .." Those conditions are completely unobtainable in my climate outside a cloche or cold glass house. And all the common bulbs thrive here. It rather depends on what bulbs you are growing.