'Bird egg' would be a compound noun. With compound nouns are we have two uninflected nouns put together: xy. (Uninflected in that we have no genitive 's malarkey or suchlike). 'y' is what the thing is. 'x' tells us kind of 'y' we're talking about. So 'duck egg' or 'ostrich egg' are more specific than simply 'egg', in that they specify what type of egg it is. Likewise 'birdbath' and 'bird table' specify that these are types of baths and tables used for birds. These slightly unusual objects need to have 'names', to distinguish them from more 'ordinary' eggs, baths and tables, so we invent compound nouns to name them. Most of the time when we are talking about eggs in general, we expect them to come from birds, so we don't need to create a special compound noun 'bird egg'. It almost goes without saying - at least in a culinary context - that an egg will be of avian origin. In the rare cases where we have to distinguish between a 'regular' egg and a crocodile egg, for example, we have no handy compound noun at our disposal, so we resort to the slightly clumsier genitive form, 'bird's egg'. That's my poultry ... I mean paltry ... two penn'orth, anyway.

The Japanese prize fish eggs (roe) above bird eggs. Tom Parker Bowles, the son of the Duchess of Cornwall, writes about plover's eggs, a delicacy which is now prohibited by law, though it was available in Evelyn Waugh's time and he duly let Lord Sebastian Flyte serve them in "Brideshead Revisited". Tom, however, writes about goose eggs and ostrich eggs as well. The BBC gives recipes for quail's egg dishes, but Wikipedia thinks it should be quail egg. So, what's correct? What would the Duchess say?

Bird eggs are eggs belonging to birds - more generic Bird's egg belong to those birds that you have specified like: those birds.' eggs i had are not as ordinary as any bird egg . Just a shot , pal ) Good question.

bird egg "sounds" wrong and I have never heard or read it before. I suppose the phrase "bird egg" could be used if you were talking about a variety of "eggs" and wanted to distinguish between those of birds and those of other creatures but I still think you would use "bird's egg" or "birds' eggs' Others may be able to provide a more coherent explanation.

I honestly think it depends on how you use it. I would say "a bird egg" when I'm talking about it generally, for example: A bird egg can be white. And I would say "this bird's egg" when I'm talking about an egg from a specific bird, for example: This bird's egg is small and white. Hope it makes sense!