Dispensationalism is a relatively new theological development. It first hit the scene when a Protestant pastor by the name of Darby (one of the "Plymouth Brethren) developed it in late 19th century.
Catholics believe in dispensations too --- BUT --- in an entirely different way than Dispensationalist Protestants do. For example, we will say that the Old Covenant was a dispensation that was followed by another dispensation in the New Covenant. They are two very broad periods of salvation history whereby God developed and revealed in the New what was hidden in the Old.
But we don't have all the various divisions in the New Covenant that Dispensationalist Protestants do.
And, we do believe in a "rapture" of sorts...but...again...not in the same way that Dispensationalists believe in one. For example, we believe that when Jesus Christ comes again (at "The Second Coming") that those who are alive in Christ (in a state of grace) will not experience death, but rather will be ushered directly into heaven. So...we do believe in a sort of rapture even if we don't use the term "rapture."
What we don't believe is that Jesus will come again, rapture up the Christians, establish a literal 1,000 year reign as King on a Throne in the new Temple in Jerusalem, after which Satan will be loosed once again for the final battle of Armageddon and finally climaxing in Christ coming (a third time?) at the end of time and vanquishing Satan and his minions into the lake of fire forever.