Mealworms

Live mealworms. We strain them from the bran they came in.

We feed our bluebirds live mealworms, which they find irresistable. Mealworms (technically the larvae of a beetle) are available in quantity from internet websites and from pet stores which usually sell smaller quantities. If your order needs to be shipped, be aware that most sources only ship early in the week, they do not want to ship so the live mealworms would sit in a hot warehouse over the weekend, they might expire in the heat.
If you order a quantity, it would usually come with the mealworms in a mesh bag with newspaper inside the bag. You can take the mealworms out of the bag and put them in a plastic container (with airholes) with something to eat, like a few pieces of apple, or some cornmeal. You can store them in the refrigerator, they become rather dormant when cold.
We ordered some from the internet, and also bought some from a pet store. The ones from the pet store came in a container with bran. So we put them in a strainer and shook it to remove most of the bran.
Bluebirds would eat practically as many mealworms as we put out. We try and offer them just several times a day, usually at the same time. During the very wet, cool spell we had, we offered more mealworms. That's because bluebirds found it hard to hunt insects, since the cold depressed insect activity. In the morning the bluebirds are lined up by the feeder, waiting for us.
We mainly offer mealworms during bluebird nesting, when they can use it most. They feed the mealworms to the nestlings. Our experience is, once the young fledge from the nest, the parents move far them away into the woods, presumably to a safer area than the open space here. They do not continue to come for the mealworms. Other people may have different experiences, do you?