For how long does it take for pink eye to spread?

Conjunctivitis. Viral conjunctivitis is very contagious often for 10-12 days depending on the virus. Protect others by washing your hands, avoid contact, sharing towels, avoid rubbing your eyes.
Around a week. While pink eye has a number of causes, the most common is infection with adenovirus, of which there are 53 serotypes. It can also cause a febrile respiratory illness. Studies of military recruits exposed to adenovirus in their living quarters indicates that it generally takes around a week before they generally show signs & symptoms. The virus is hardy & can live on doorknobs, towels, for weeks.