One of the ways to study finitely generated residually finite groups is by examining various growth properties, such as word growth and subgroup growth. A related recently studied property is normal residual finiteness growth, which quantifies how large of a finite quotient is needed to detect an element of the given group. This growth is known to be polynomial for linear groups over any characteristic, and I will provide a uniform bound for linear groups that depends only on the degree of linearity and not the field of coefficients. I will also briefly discuss non-normal residual finiteness growth, which involves an element avoiding any subgroups of finite index up to a given size instead of just normal subgroups, and give some results concerning linear groups. In particular the exact growth rate is given for Chevalley groups over specific rings.