He was born in Fellin (now known as Viljandi) in the Livonian Governorate of the Russian Empire (present-day Estonia).
Afterwards, he was an assistant to Friedrich Albert von Zenker (1825–1898) at the pathology institute in Erlangen.
In 1890, Bostroem reportedly isolated the causative organism of actinomycosis from a culture of grain, grasses, and soil.
Following Bostroem's discovery, there was a general misconception that actinomycosis was a mycosis affecting individuals who chewed grass or straw.
The agents of actinomycosis are now known to be endogenous organisms of the mucous membranes, most commonly Actinomyces israelii, a species named after surgeon James Israel, who first discovered its presence in humans in the late 1870s.