According to the wiki page, which references Journal 3, the bunker was indeed built by Ford Pines. It was intended as a safehouse, an alternative location to carry out experiments, as well as to contain the shapeshifter.
This is different from the laboratory under the Mystery Shack (and Ford's private study was), where he carried out the majority of his experiments.
Both were built by Ford. The difference is that while hidden, the one under the shack was still in a known place, where all you'd need to do is know to look or dig around to find it. The one beneath the tree on the other hand was much more secluded and unsuspecting place, and thus more difficult to find, making it a better "safehouse".