Does marx have asssumptions about bourgeoisie?

Marxism created the term "Bourgeoisie" that we know today, or rather, Marxism created the connotations of the term.

So, the definition of "Bourgeoisie" would be Marxist theory based on factual events during the rise of Capitalism. So, no Marx did not really have "assumptions".

Also, keep in mind that Marxism and Marx are two different things, although, people often view them as interchangeable. After Marx passed away, other theorists redefined elements of Marxism. Also, it is difficult to determine Marx's exact opinion, when many of his works were co-written with his colleagues. Even the Communist Manifesto was co-written with Friedrich Engles.