At the age of 14 he became a student of Bartholomeus van Hove and painted in his studio along with Van Hoves son Hubertus van Hove. Together they worked on the pieces of scenery that Van Hove created for the Royal Theatre in The Hague. In addition, Bosboom took lessons from 1831 to 1835 and again from 1839 to 1840 in the Hague Academy of Art. Here he also made the acquaintance of Anthonie Waldorp and Wijnand Nuyen.
The young Bosboom traveled to Germany in 1835 to Düsseldorf, Cologne and Koblenz and painted the watercolor View of the Mosel Bridge at Koblenz. This painting was purchased by Andreas Schelfhout, who became his confidante and friend. In 1839 he traveled to Paris and Rouen and received a silver medal for View of the Paris Quay and the Cathedral at Rouen. He also painted a number of church interiors, a relatively traditional genre in which the seventeenth century artists Pieter Saenredam and Emanuel de Witte served as important examples. Bosboom had a great deal of success with these pieces, and for the rest of his career he would repeatedly return to this theme, which was the one in which he would achieve his greatest fame.