Probably by John Adams & Co, c.1870-1900, after L.F. Roubiliac
This bust of Wesley is based on a marble bust modelled by Louis-François Roubiliac (1702-1762), a talented French sculptor who worked in London in the mid -18th century. The original is thought to have been worked around 1750-60, and Wesley is notably younger in this portrayal than in Enoch Wood's bust of 1781.
Wesley was an admirer of Roubiliac's work, referring to the artist's monument of Lady Elizabeth and Joseph Nightingale in Westminster Abbey as the finest in the Abbey, 'as if the marble could speak'.
See also Enoch Wood's bust of John Wesley in the online Collection.