Wikipedia offers this thought:
Contemporarily, the terms "bourgeoisie" and "bourgeois" identify the ruling class in capitalist societies, as a social stratum; while "bourgeois" describes the [worldview] of men and women whose way of thinking is socially and culturally determined by their economic materialism and philistinism, a social identity catalogued and described in drame bourgeois (bourgeois drama), which satirizes buying the trappings of a noble-birth identity as the means climbing the social ladder. (See: Le Bourgeois gentilhomme, 1670.)
The sources noted are:
- Benét’s Reader’s Encyclopedia Third Edition (1987) p. 118, p. 759.
- Molière, ed. Warren 1899
It's opening paragraph also contains this matching description:
As such, in the Western world, since the late 18th century, the bourgeoisie describes a social class "characterized by their ownership of capital, and their related culture"; hence, the personal terms bourgeois (masculine) and bourgeoise (feminine) culturally identify the man or woman who is a member of the wealthiest social class of a given society, and their materialistic worldview.
Looking the word up in a standard dictionary mildly supports this:
the middle classes
(in Marxist thought) the ruling class of the two basic classes of capitalist society, consisting of capitalists, manufacturers, bankers, and other employers. The bourgeoisie owns the most important of the means of production, through which it exploits the working class
More on the Marxist usage can be found at this Marxist glossary.
In terms of using it properly, it sounds as if the word is tremendously charged with controversy and economic debate. I would avoid using the term unless you were discussing the specific theories involved or are seeking to annoy someone who happens to dislike Marx.
In American English, appropriate alternatives would be middle class, upper-middle class or upper-class depending on your intended usage. You can read the Wikipedia links for more information.