"Silk of the kine and poor old woman" are both names given to Ireland "in old times," so Stephen is thinking of the old milkwoman as a mythical representative of the nation.
The first phrase, from the Irish a shíoda na mbó, means “the most beautiful of cattle” (Gifford, 21). The tSean-bhean Bhocht or Shan Van Vocht, a legendary figure from a 1790s ballad, looks like a poor old woman to most, but to true patriots appears as a beautiful young queen. In this instance it seems that no true patriots are present, for we see only the “lowly form of an immortal serving her conqueror [Haines] and her gay betrayer [Mulligan].” And when Haines tries speaking some Irish to her, she mistakes it for French.
The Shan Van Vocht had been particularly on people's minds since 1895, when two young Ulster women, Alice Milligan and Anna Johnston, founded a monthly journal with that title. The journal was published in Belfast from January 1896 to April 1899. It aimed to promote the centenary celebration of the 1798 Rising and to advance the nationalist cause of decolonizing Ireland. It also published items of poetry, fiction, history, folklore, and other cultural content consistent with the aims of the Irish Revival. Alice Milligan in particular was a poet of some repute and a well-known figure in Dublin. The magazine was distributed throughout Ireland. For more on the political importance of this journal, see Nora Shovelin's unpublished masters thesis, Political Communication in the Shan Van Vocht Magazine, 1896-1899: An Example of Print Culture, A Media-Product with Action-Value (2005).
Stephen does not have a good relationship with the Poor Old Woman. Here he looks at the milkwoman as a kind of goddess who may have a message for him, "but scorned to beg her favour." Soon he is resenting her attention to Mulligan and Haines, and later in Telemachus he appears to think of Ireland as "A crazy queen, old and jealous," who "wants me for odd jobs." In Circe the figure comes back as Old Gummy Granny, a fiercely nationalistic crone who urges Stephen to fight and die for his country.