  We study by Monte Carlo simulations the influence of bond dilution on the
three-dimensional Ising model. This paradigmatic model in its pure version
displays a second-order phase transition with a positive specific heat critical
exponent $\alpha$. According to the Harris criterion disorder should hence lead
to a new fixed point characterized by new critical exponents. We have
determined the phase diagram of the diluted model, between the pure model limit
and the percolation threshold. For the estimation of critical exponents, we
have first performed a finite-size scaling study, where we concentrated on
three different dilutions. We emphasize in this work the great influence of the
cross-over phenomena between the pure, disorder and percolation fixed points
which lead to effective critical exponents dependent on the concentration. In a
second set of simulations, the temperature behaviour of physical quantities has
been studied in order to characterize the disorder fixed point more accurately.
In particular this allowed us to estimate ratios of some critical amplitudes.
In accord with previous observations for other models this provides stronger
evidence for the existence of the disorder fixed point since the amplitude
ratios are more sensitive to the universality class than the critical
exponents. Moreover, the question of non-self-averaging at the disorder fixed
point is investigated and compared with recent results for the bond-diluted
$q=4$ Potts model. Overall our numerical results provide evidence that, as
expected on theoretical grounds, the critical behaviour of the bond-diluted
model is governed by the same universality class as the site-diluted model.
