We consider the behaviour of semi-oriented bootstrap percolation restricted to a finite square or torus. We prove that as the probability of initial occupancy p tends to zero, the side length required for a two-dimensional torus to have non-negligible chance of filling itself up is between e( c l o g 2 p ) / p and e( C l o g 2 p ) / p for universal constants c and C. We show similar results for the side length required for a square to show significant clustering behaviour.