We study approximation algorithms for the forest cover and bounded forest cover problems. A probabilistic $2+ε$ approximation algorithm for the forest cover problem is given using the method of dual fitting. A deterministic algorithm with a 2-approximation ratio that rounds the optimal solution to a linear program is given next. The 2-approximation for the forest cover is then used to give a 6-approximation for the bounded forest cover problem. The use of the probabilistic method to develop the $2+ε$ approximation algorithm may be of independent interest.