I'd feel safer with a hitch around the tree. I think the tree sap could corrode the eyed bolt, if it did you could take a fall.
Whenever I go up a tree I use a throwline and weight, put it over a good limb or fork well above where the stand is, using a running bowline, use the rope to ascend to the stand leaving myself attached to the rig, then repelling down on the same rope when I'm ready to leave. I tie the throwline into the bowline before running it up, that way I can retrieve my climbing rope once I'm on the ground.
If you can find a good horizontal limb, you won't even need a stand in the tree, just let your harness support part of your weight, and the limb part of your weight. With a good harness it's actually pretty comfortable.