He trained under the Huguenot James Basire the younger (1769–1822) before spending several years in Rome, where he came to know J. M. W. Turner, Frederick Catherwood and Bertel Thorvaldsen.
[1] While in Rome he made some excellent copies of celebrated pictures, and acquired great facility as a draughtsman.
His plates, which are all from pictures by popular English painters of the day, include 'The Meeting of the Council of the Anti-Corn Law League,' after J. R. Herbert; 'Heather Belles,' after John Phillip; 'The Council of War in the Crimea,' after Augustus Egg; 'The Gentle Warning,' after Frank Stone; 'The Heart's Resolve,' and 'The Momentous Question,' after Sarah Setchell; 'Milton composing "Samson Agonistes,"' after J. C. Horsley; 'Opening of the Great Exhibition of 1851,' after H. C. Selous; 'Salutation to the Aged Friars,' after C. L. Eastlake; 'Dr.
Johnson's Visit to Garrick,' after E. M. Ward; and portraits of Albert, Prince Consort, Lord John Russell, and the M.P.
Bellin drew and etched on three plates a panoramic view of Rome from Monte Pincio, which he published, with a dedication to Prince Augustus Frederick, Duke of Sussex, in 1835.