We propose an alternative inflationary universe scenario in the context of Randall-Sundrum braneworld cosmology. In this new scenario the existence of extra dimension(s) plays an essential role. First, the brane universe is initially in the inflationary phase driven by the effective cosmological constant induced by a small mismatch between the vacuum energy in the five-dimensional bulk and the brane tension. This mismatch arises since the bulk is initially in a false vacuum. Then, false vacuum decay occurs, nucleating a true vacuum bubble with negative energy inside the bulk. The nucleated bubble expands in the bulk and consequently hits the brane, causing a hot big-bang brane universe of the Randall-Sundrum type. Here, the termination of the inflationary phase is due to the change of the bulk vacuum energy. The bubble kinetic energy heats up the universe. As a simple realization, we propose a model in which we assume an interaction between the brane and the bubble. We derive the constraints on the model parameters taking into account the following requirements: solving the flatness problem, no force which prohibits the bubble from colliding with the brane, a sufficiently high reheating temperature for the standard nucleosynthesis to work, and the recovery of Newton's law up to 1 mm. We find that a fine-tuning is needed in order to satisfy the first and the second requirements simultaneously, although the other constraints are satisfied in a wide range of the model parameters.