Ferroelectric domain nucleation and growth in multiferroic BiFeO3 films is observed directly by applying a local electric field with a conductive tip inside a scanning transmission electron microscope. The nucleation and growth of a ferroelastic domain and its interaction with pre-existing 71^{∘} domain walls are observed and compared with the results of phase-field modeling. In particular, a preferential nucleation site and direction-dependent pinning of domain walls is observed due to slow kinetics of metastable switching in the sample without a bottom electrode. These in-situ spatially-resolved observations of a first-order bias-induced phase transition reveal the mesoscopic mechanisms underpinning functionality of a wide range of multiferroic materials.