Put the rabbit bones and 7 cups water into a medium pot and bring to a rolling boil over medium-high heat. Reduce heat to medium-low and simmer for 30 minutes. Skim and discard any foam and impurities that float to the surface.
Add the carrots, celery, onions, parsley, and bay leaf to the pot and gently simmer, partially covered, for 2 1⁄2 hours.
Strain the stock through a fine-mesh sieve set over a large bowl or medium pot, pressing the solids to extract as much liquid as possible; discard solids. Strain the stock once again through the sieve lined with 2 layers of cheesecloth, if you'd like a clearer stock. Season to taste with salt. Set the bowl or pot of stock over an ice bath to let cool, uncovered. Cover and refrigerate. Skim any congealed fat from surface when ready to use.