A specific answer would depend on the specific country, but generally Bolshevism was feared because if the workers, led by the Bolsheviks (communists) carried out their threatened revolution then the middle class would lose their political power and their wealth. This would mean that "the rich" would no longer control the country and would not be able to make huge profits from their businesses by paying the workers (low wages) a small percentage of what the company earned.
In countries like Russia where the first successful Communist revolution occured, even bigger changes would be needed as the country was ruled by a king (Tsar) so not just the middle class would lose out but so would all the royalty and nobles.
Bolshevism threatened to change the way countries had always been and so it was seen as REALLY scary by anyone with any power or wealth that they could lose.