No, a blue bird is not a bluebird. A bluebird is a type of American thrush, and there are no bluebirds in Britain where the novel you cite from is set. This is a bluebird:
as is this:
Those are both bluebirds. There are no bluebirds in Europe, only in North America.
The famous color “robin’s egg blue” refers to the American robin, not to the European one, whose eggs are the wrong color.
Furthermore, the robins of Europe are not thrushes, and do not have the blue eggs characteristic of the American robin. Rather, they have eggs that look like this:
bits of blue bird’s eggshell
is applying blue to bird’s eggshell. So it is the blue eggshell of some bird.
It is possible that it is shell of the Common Blackbird, a European turdid and thrush whose eggs look like this:
The so-called “Common Blackbird” acts just like an American Robin, whose genus it shares. It rather looks like its cousin, too. It just has a solid brownish black breast, not the redbreast that our own Robin is so famous for. (Which is in fact orange, but why we are calling orange red—well, that’s another tale.)