It can take months or years. Research has shown that it typically takes years, but more rapid progression is possible as well, as many of us on this board have experienced. You should definitely keep up with your Paps as your doctor recommends.
Personally, mine progressed from CIN I to CIN III in just 6 months.
It depends on what stage dysplasia you have. Mild dysplasia usually will regress, where as moderate and severe have a greater chance of progressing to cancer.I think it would be important to have an HPV test to rule out high risk strains that are commonly found in cervical cancer. Ive heard that cervical cancer can take years so if you get your yearly paps early detection is on your side.
It's also important to know that not all dysplasia will progress into cervical cancer, many dysplasia can regress on their own without medical intervention. Even moderate dysplasia (CIN2) and severe dyplasia (CIN 3 and CIS) will not always progress but because it is impossible to know who will progress and who won't, it is extremely important to either monitor it or remove it depending on the severity.