The bourgeoisie is the exploiter class most characteristic of the capitalist system. The word "bourgeoisie" is a plural noun. We use the word "bourgeois" as an adjective and occasionally as the singular noun.
Before there was capitalism in Western Europe, there was feudalism. In French feudalism, the term "bourgeoisie" arose to refer to the middle-classes of the cities, people who traded or other men of wealth but not the highest social standing. The French Revolution of 1789 was the ultimate bourgeois revolution. It made the bourgeoisie the highest class. People who were rich but without the highest social standing tore down the privileges of the old upper classes in 1789.
In general the bourgeoisie brought about principles of rule that sanctified money above birthright or family ties. Having a prestigious name was no longer what brought one to the pinnacle of power under bourgeois rule.
We raise all this to point out that the "bourgeoisie" has not been the same for all of history. It has developed.
Capitalism exists where non-workers control the production of wage-workers, even if property is officially state property. Under capitalism, democracy for the working classes is undermined through people's lack of control of their own workplace and society as a whole. Workers (as distinct from petty-bourgeoisie) have little say in how their workplace is organized or what will be produced.
The term "bourgeoisie" now usually refers to the capitalist class in common usage. The capitalist class is that class of people who own enough property that they would not have to work to make a living. The capitalist class only works if it wants to. Also included in the term are people with very powerful positions in production or government generally. A ruler may or may not have great assets on hand, but if s/he really wanted them, s/he has the power to get them. For example, Ronald Reagan made a speech in Japan with a $1 million fee after he retired from the presidency. If he had been "poor" during the presidency, he still would have been part of the "capitalist class." What he was doing was central enough to the ruling class of capitalism that he had de facto access to the means of production, even if he had gambled away his ranch and other assets in Las Vegas while he was in the White House.
An overly restrictive definition of capitalist is someone who owns the means of production--factories, tools and patents for example. What is important is not the literal ownership of means of production but access to those means of production. Such access could be merely the ability to get a loan so large that it is possible to live off the business connected to such a loan. Access to political information in the military, intelligence or executive branch would make it possible to be rich making a speech like Reagan did or by selling secrets to foreigners. People with such access to information also may be bourgeoisie. For example, Reagan could take his $1 million speech fee and convert it into means of production such as ownership of tools and factory buildings. Whether he does that or not, we can say he has "access" to the means of production.
There is another common and critically important usage of the term "bourgeoisie." Technically the bourgeoisie includes other sections, including those more numerous than the capitalist class. The "petty-bourgeoisie" or "petit-bourgeoisie" refers to people who are exploiters but not on the scale of the capitalists. The petty-bourgeoisie often owns its own means of production or professional skills but does not hire enough workers to be able to quit working and still live a life of leisure. There are other categories of bourgeoisie that are not capitalist, such as what Mao called the "comprador bourgeoisie" which owes its existence to imperialist capitalists and cannot function on its own as a capitalist class.
The difference between the proletariat and the petty-bourgeoisie is a point of great difficulty today. MIM members are under obligation to quit any party that confuses the petty-bourgeoisie and the proletariat in the imperialist countries. Applying the Marxist theory of "petty-bourgeoisie" to reality is the source of difficulty.
Another meaning behind the word "bourgeois" and the reputation of the bourgeoisie derives from the pre-capitalist ruling class. In this meaning, a bourgeois is someone shallow, money-oriented and without taste that cultivated rulers should have. It is very popular to refer to bourgeois culture or bourgeois lifestyle in this sense.
When MIM uses the term "bourgeoisie," it is most likely referring to the exploiter class of the united $tates, Kanada, England etc. today. In sum, exploiters today in the imperialist countries are people who appropriate other people's labor. Small exploiters are petty-bourgeoisie and the most powerful exploiters are referred to as capitalists or just "bourgeoisie."