I know cancer is not contagious but if someone with cancer bled on a desk then how long will the cancer cells stay alive in it?

Unless it is a hematopoetic cancer, it is unlikely that there would be any cancer cells from a small amount of blood. In any event cancer cells in this siutation would be very easily killed by drying or any disinfectant (including soap and water). Regardless, no cancer cells, alive or dead, would be contagious to you in this scenario.

No longer than the time it will take for the blood to dry.