Im Lexico (vormals Oxford Dictionary) wird in den allermeisten Anwendungsbeispielen (hier nur ausschnittsweise) Großschreibung verwendet, Collins hat beide Schreibweisen :
Definition of Bildungsroman in English:
A novel dealing with one person's formative years or spiritual education.
‘the book is a bildungsroman of sorts, as Tull overcomes his abused childhood and learns about love’
‘Hughbury Shamp, a teenager with a yen for fame - note: all three novels are Bildungsromane - follows three masters whom he introduces at the beginning of his first-person account, an echo of Marcus Aurelius starting his meditations.’
‘The tendency of novel theory to define the novel as a genre that is sui generis does lead to certain impasses and quandaries, whether in the theory of the novel as such or of a subgenre like the Bildungsroman.’
‘E. L. Doctorow's Billy Bathgate is a Bildungsroman which shares many central characteristics with Updike's novel and Roth's.’
‘Do genres have typical scripts, such as rescue for the adventure novel, or going to school for the Bildungsroman, or seduction for the romance?’
‘Jane Eyre is a Bildungsroman, or a coming-of-age novel, which recounts the first nineteen years of the character of Jane Eyre, in the first-person voice.’ ...
Bildungsroman in British
a novel concerned with a person's formative years and development
Collins English Dictionary. Copyright © HarperCollins Publishers
Word origin of 'Bildungsroman'
literally: education novel
... bildungsroman in American
nounWord forms: plural ˈbilˌdungsromans
a novel that details the maturation, and specif. the psychological development and moral education, of the principal character
: also German ˈBildungsroˌman (ˈbɪldʊŋksrɔˌmɑn ) Word forms: plural German ˈBildungsroˌmane (ˈbɪldʊŋksrɔˌmɑnə ) ...