Both shrews and moles are carnivores and would not be interested in any kind of plant material. They would be interested in insects and earthworms, however. The culprit that ate your bulbs was probably a vole. Voles often use the burrows made by moles, eating any plant roots or bulbs that the mole has left exposed while it was digging for worms.
You can make wire cages out of wire mesh to enclose each of your tulip bulbs and iris rhizomes when you plant it. If you prefer, you can enclose the entire bed by placing wire fabric over the bottom and around the sides. Place it over the top of bulb beds, too. The tops of iris rhizomes grow above the surface of the soil, so it would be pointless to cover them with wire mesh.
I recommend welded wire fabric for this purpose, although many people use chicken wire. The problem is that young voles are quite small (think mouse-sized) and can easily fit through the openings in chicken wire. Chicken wire does work well for larger rodents, such as ground squirrels, adult rats, and groundhogs.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams