We present some results on the distribution of zeros of functions in the Bers space $Q(\mathbb{D})$, showing how the distribution depends on the bounds of the growth of $|f(z)|$ as $|z|\to1$, for $f\in Q(\mathbb{D})$. We also exhibit an open and dense subset, $M\subset Q(\mathbb{D})$, which has the property of uniform control over the number of zeros in disks of hyperbolic radius 1 contained in $\mathbb{D}$.