A bismuth-germanate (BGO) escape-suppression shield for the high-purity germanium triple-cluster detector of the MINIBALL $ \gamma$ -ray spectrometer was designed and built. Monte Carlo simulations with the simulation code GEANT4 were performed to guide the construction and to determine the detector geometry of the new BGO shield. After the first measurements concerning mechanical properties of the BGO housing and the performance of the photomultiplier tubes at the Institut de Physique Nucléaire, Orsay, the prototype BGO escape-suppression shield was combined with a MINIBALL triple-cluster detector at the Institut für Kernphysik, Cologne. A dedicated electronics and digital data-acquisition system was put into operation in order to determine timing properties of the combined coincidence measurement and to measure values for the energy resolution of the BGO detectors, for the BGO low-energy threshold, and for the crucial peak-to-total ratio (P/T). The measured P/T value for a standard$^{60}$Co $ \gamma$ -ray source compares well with expectations and will allow to proceed with the amendment of the MINIBALL triple-cluster detectors with an escape-suppression shield for improved in-beam $ \gamma$ -ray spectroscopy especially at the new HIE-ISOLDE accelerator for radioactive ion beams at CERN.