Bootstrap percolation is a model in which an element of $\mathbf{Z}^2$ becomes occupied in one time unit if two appropriately chosen neighbors are occupied. Schonmann [4] proved that starting from a Bernoulli product measure of positive density, the distribution of the time needed to occupy the origin decays exponentially. We show that for $\alpha > 1$, the exponent can be taken as $\delta p^{2\alpha}$ for some $\delta > 0$, thus showing that the associated characteristic exponent is at most two. Another characteristic exponent associated to this model is shown to be equal to one.