"Our" blackbirds are expert at digging up bulbs - I have watched them do it. They scratch the soil, see the little tuft at the top of the bulb and tug at it until its on the surface. Presumably its a disappointment that its not a worm as they first thought!
I think that SlackAlice is probably right, we have foxes in the garden and the bulbs are recently planted ones. Definitely not birds or squirrels as it happens at night! Thanks all!
Do you have cat's where you live? If the soil has recently been dug over to plant these bulbs, Cat's love to mess about in the soil and dig about in it.