Bertel Müller apprenticed as a pharmacist in Aalborg and then moved to Copenhagen where he graduated as candidates pharmacies in 1858. He worked for a year in Randers and was then employed by Alfred Benzon, the founder of Alfred Benzon A/S, at the Swan Pharmacy in Copenhagen in 1859.
Bertel Müller and Alfred Benzon opened a shop with photography equipment at Bredgade 21 in 1862. It was converted into a photographic institute with student programs in 1863. Alfred Benzon left the company in 1866. Müller was instead joined by the art historian Philip Weilbach until 1871, and from then on owned Budtz Müller & Co. alone. The firm offered a wide selection of high-quality stereoscopies and photographs in large and small formats from Copenhagen. Other images were of prominent cultural figures such as Grundtvig, Hans Christian Andersen, actors in costumes, works by Bertel Thorvaldsen and 33 stereoscopies from Greenland recorded in 1866.
Bertel Müller collaborated with Jean Christian Ferslew in introducing photolithography to the Danish market and created the first photolithographic maps for the Danish General Staff, as well as a number of reproductions of manuscripts for the Arnamagnæan Institute. Bertel Müller and Ferslew published Gotfred of Ghemen's print from 1495 of Den danske Rimkrønike in 1873.
Bertel Müller was in 1869 appointed as Swedish and Norwegian court photographer and in 1870 also as Danish court photographer. He wrote a number of articles about the history of photography in Den fotografiske Forenings Tidende in 1865.
Müller married Maren Christine Petersen (1840-1878), a foster daughter of dyer Hans Nikolaj Edinger Grundtvig (1807-1887) and Anna Marie Petersen (1804-1865), on 4 December 1863 in the Church of Our Lady in Copenhagen.