The length you can prevent your period using a monophasic birth control pill or ring will depend on the person. From my experience, the first time you try monophonic birth control, about 3 months. Then each time it goes farther. But everybody is different. Indefinitely e.g. years! It will NOT affect your future fertility.
A good read is John Rock’s Error by Malcolm Gladwell on how it’s not necessary to have a period while on the pill. The withdrawal bleed was just put there because one of the creators of the pill was a devout Catholic and wanted to use the pill with the rhythm method.
Read more facts and learn how to skip your period here.