The use of bioactive glass (BG) particles as a filler for the development of composite electrospun fibers has already been widely reported and investigated. The novelty of the present research work is represented by the use of benign solvents (like acetic acid and formic acid) for electrospinning of composite fibers containing BG particles, by using a blend of PCL and chitosan. In this work, different BG particle sizes were investigated, namely nanosized and micron-sized. A preliminary investigation about the possible alteration of BG particles in the electrospinning solvents was performed using SEM analysis. The obtained composite fibers were investigated in terms of morphological, chemical and mechanical properties. An in vitro mineralization assay in simulated body fluid (SBF) was performed to investigate the capability of the composite electrospun fibers to induce the formation of hydroxycarbonate apatite (HCA).