Conservative or Bourgeois Socialism was a term used by Karl Marx and Friedrich Engels in various pieces (including in the Communist Manifesto).
The Marxian view is such that the bourgeois socialist is the sustainer of the current state of bourgeois class relations. Opinions vary as to whether this or that bourgeois socialist intentionally is excusing the current order but the common thread is that they are, in objective fact, preserving it. Rather than abolishing class divisions, they wish to simply raise everyone up to be a member of the bourgeoisie, to allow everyone the ability to endlessly accumulate capital without a working class. In the Communist Manifesto, Marx and Engels use philanthropists, monks ("temperance fanatics"), and reformers as examples of this type of socialist that they saw as opposed to their own aims.
In this class, Marx explicitly referenced Proudhon's The Philosophy of Misery, stating:
||The Socialistic bourgeois want all the advantages of modern social conditions without the struggles and dangers necessarily resulting therefrom.