Let $(G_t)_{t\in T}$ be a centred Gaussian process with canonical semimetric $d_G$. Assume the process is separable with respect to $d_G$, and let $\overline{T}$ denote the metric completion of the quotient of $T$ by the relation $d_G(s,t)=0$. If \begin{align*} \int_0^{\operatorname{diam}(T,d_G)}\sqrt{\log N(T,d_G,\varepsilon)}\,d\varepsilon <\infty, \end{align*} then there is a version of the process that extends to $\overline{T}$ and has bounded sample paths on $\overline{T}$ with probability one.