The Bloch-sphere representation is a rather simple geometric model for all possible quantum states of a two-level system. In this article, we propose a simple geometric model for the time dynamics of a qubit based on the Bloch-sphere representation. The model can be applied both to time-independent and time-dependent Hamiltonians. As explicit application, we consider time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing-UP of the quantum emitter population) in the context of quantum tunneling. We show that the tunneling probability can be enhanced by orders of magnitude when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call educator-developer dialogue, an updated version of the software Quantum Composer is presented. Here it is used for educational purposes, to map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.