In this work, we introduce the embedded microbubble, a novel PDMS-based microstructure combining the low power advantage of bubble-based acoustic streaming with the temporal stability of acoustically-excited solid features. We perform in-depth numerical investigations and quantify the influence of geometrical parameters, such as the PDMS wall thickness or the microbubble's length, on the acoustic streaming inside the fluid channel and utilise these findings to optimise our device design. The manipulation capabilities of our acoustofluidic lab-on-chip are analysed through experimental characterisations and the revealed insights are discussed in further detail with respect to the numerical results. Finally, we highlight our device through the controlled and reliable out-of-plane rotation of single HeLa cells; a task beneficial to improve our understanding of biological processes on the cellular and sub-cellular level, and demonstrate the relevance of our approach for additional microfluidic applications through its use for mixing; a key step required for a wide variety of biomedical as well as chemical research.