2-3 times the diameter of the bulb, Snowy. Deeper in sandy soil, and shallower in clayish soil--they don't like really heavy clay.

hi there i planted alliums in my back garden and its fairly clay/ sandy once you get past the topsoil and they all came up am sure that tuqbrethil is right that they dont like ...but just wanted to encourage you in case you have clay soil ... good luck with your alliums .. alison

Sorry, no discouragement intended! Even if the soil is heavy clay there are a lot of things you can do to fix it:

Mix in coarse sand and organic matter, about 1 part sand, 1 part organic matter (like compost), to 2 parts soil.
Also maybe add gypsum--it makes the clay particles stick together in sand-sized clumps (flocculation). Especially effective near the sea shore, where the soil might be salty.
If worse comes to worst, build raised beds, and replace the soil with good topsoil.

I also wish you well on your Alliums, Snowy!