This trick dates back at least to the thirteenth century; see Al-Jawbari’s Al-Mukhtār fi Kashf al-āsrār, c. 1232–1249. Al-Jawbarī's description of the Egg Bag is translated in Pierre Tailler’s “From Baghdad to Córdoba” in Gibecière, Vol. 17 No. 2, Summer 2022, p. 25.
The small form of Egg Bag, as is generally used in modern times, is credited to Herbert Albini (Abraham Laski), in the late 1800s.
The Mesh or Net Egg Bag
A variant Egg Bag design featuring a net corner, allowing the egg to be seen inside the bag, began appearing on dealers' shelves by 1900, attributed to Hiam; see, for example, Ellis Stanyon advertisement in Magic, Vol. 4 No. 11, Aug. 1904, p. 106. In a little over twenty years, the corner was expanded until the entire front panel of the bag was made of mesh; see Heaney's Catalog No.25, 1924. This open-fronted Egg Bag has been attributed to C. H. Larette (Cornelius Hauer, 1889-1943). Other variations took the meshing across just the width of the bottom of the bag.
See also: Climax Egg Bag.