A c-section scar may be horizontal or vertical, and it usually sits right above your pubic hairline, so you should still be able to wear a bikini (yay!).
It will take between four and six weeks for the incision to heal, and it will likely fade over time—just how much will depend on your genes (some women are more likely to have excess scar tissue). Sorry, but it will never be completely invisible. You can help it along with a scar-fading ointment like Mederma.