Bring stock, water, celeriac, potatoes, apple, shallot, bay leaf, and 1 teaspoon salt to a boil in a large pot. Cook until tender, about 10 minutes. Strain, reserving liquid; discard bay leaf. Return celeriac, potatoes, apple, and shallot to pot, and add 3/4 cup reserved cooking liquid. Coarsely mash with a potato masher.
Using a fork, mash together butter and blue cheese in a small bowl. Stir into celeriac mixture. Season with salt. (Mash can be made up to 1 hour ahead; transfer to a heatproof bowl, cover, and set over a pan of barely simmering water, stirring occasionally.)
Spoon into a warm serving bowl, and crumble blue cheese over top.