Varies with the size of the bulb - there is usually guidance on the packaging, but roughly twice or two and a half times the depth of the bulb.

Personally I plant them 3x the depth of the bulb.

It is not really critical as most bulbs can and do move themselves up and down in the soil to the depth they like.
Funny thing is though that we have a large number of self seeded bulbs of various kinds and almost all of them are on the sruface or just below and growing happily, even after this feeezing winter.

We've got the same Owdboggy

Today I was attempting to weed a bit and there are 1,000's of Galtonia bulbs just under the multch. And they are supposed to be slightly tender!

My experience with most bulbs indicates that when in doubt, plant a little too shallow, rather than a little too deep. The main exceptions seem to be tulips, especially species tulips.