He settled in New York City in 1879, doing his first work there for Charles Scribner's Sons, and the next year travelled to Venice, where he executed pen drawings and watercolours.

His pen-and-ink work for the Century Magazine attracted wide attention, as did his illustrations for Sir Edwin Arnold's Japonica.

His oil painting The Venetian Beadstringers (1889) was a popular work, which, when shown at the National Academy of Design, resulted in him being elected an Associate.

Blum's chief patron, Alfred Corning Clark, heir to the Singer Sewing Machine fortune, commissioned twin canvasses, 50 feet long and 12 feet high, for the proscenium of Mendelssohn Hall in downtown New York, which he had constructed to house the famous Mendelssohn Glee Club.

These works went missing when the Hall was demolished in 1912, but were later found in the vaults of the Brooklyn Museum, which put them on temporary display for the 100th anniversary of the Glee Club in 1966.