House cats and raccoons are the most common animal predators. The best way to protect bluebirds from these predators is to mount the nest box on a metal or pvc pole. Cats can not climb these poles. If raccoons are a real threat, multi-purpose lithium grease on the poles works great. This may also help to deter snakes.
Bluebirds are really grassland birds.
It is difficult to attract them to urban or heavily wooded property. Most bluebirds prefer open fields with one or two large oak trees, pastures, vineyards, old orchards or large mowed yards with selected medium-sized trees for nest guarding. Nest boxes should be placed out in the open on fence posts or metal poles not nestled into groves of trees. Bluebirds are primarily insect eaters. They do like berries, but they are rarely attracted to the typical bird feeding stations that offer a variety of seeds.