I feed the birds and put out plenty of sultanas, chopped apple and oats for the blackbirds, but I can't provide what's best for them - worms - they have to find those themselves, and they do.
I love to watch the blackbirds rootling around in my borders for worms - it means my soil must be in pretty good heart. After all, sweeping some bark mulch back off the path every few days isn't really that onerous is it? Far better than starving birds IMHO.
As for digging up plants and bulbs
unless your bulbs are planted far too shallowly, or you've seen a blackbird with a trowel under his wing, it's unlikely to be them - far more likely to be pesky grey squirrels - plant your bulbs deep and in 'bags' made of small mesh chicken wire' - that'll stop the little blighters.