  Since their introduction in 1997, the Hardy spaces of Dirichlet series have
been broadly and deeply studied. The increasing interest sparked by these
Banach spaces of Dirichlet series motivated the introduction of new such
spaces, as the Bergman spaces of Dirichlet series $\mathcal{A}^p_{\mu}$ here
considered, where $\mu$ is a probability measure on $(0,\infty)$. Similarly,
recent lines of research have focused their attention on the study of some
classical operators acting on these spaces, as it is the case of the Volterra
operator $T_g$. In this work, we introduce a new family of Bloch spaces of
Dirichlet series, the $\text{Bloch}_{\mu}$-spaces, and study some of its most
essential properties. Using these spaces we are able to provide a sufficient
condition for the Volterra operator $T_g$ to act boundedly on the Bergman
spaces $\mathcal{A}^p_{\mu}$. We also establish a necessary condition for a
specific choice of the probability measures $\mu$. Sufficient and necessary
conditions for compactness are also proven. The membership in Schatten classes
is studied as well. Eventually, a radicality result is established for Bloch
spaces of Dirichlet series.
