In the theoretical description of the neoclassical tearing mode the bootstrap current is assumed to completely vanish inside the magnetic island if finite perpendicular transport can be neglected. In this paper, the effects due to both the finite-orbit width of the trapped ions and their toroidal precession (not included in the standard analytic theory) on the island current are investigated. The evolution of the ion distribution function in toroidal geometry in the presence of a perturbed magnetic equilibrium is computed numerically employing the deltaf method, collisions being implemented by means of a Monte Carlo procedure. It is shown that a significant fraction of the (ion) bootstrap current survives inside the island when the ion banana width wb approaches the island width W, and no loss is observed for wb/Wgeq1. This effect is reduced when the collision time becomes longer than the toroidal drift time. The value of the current is found to be inconsistent with the local gradients in the island region. The finite-banana-width effect leads to a linear scaling of the value of the poloidal beta at the mode onset with the normalized ion poloidal gyroradius rhoastp, in agreement with the experimental results of ASDEX Upgrade.