Using global MHD simulations of the solar wind-magnetosphere--ionosphere system, we investigate the depen-dence of the contribution from the Earths bow shock (I1bs) to ionospheric region I field aligned current (FAC) (I1). It is found that I1bs increases with increasing southward interplanetary magnetic field (IMF) strength Bs, if the Alfven Mach number MA of the solar wind exceeds 2, a similar result as obtained by previous authors. However, if MA becomes close to or falls below 2, I1bs will decrease with B8 in both magnitude and percentage (i.e., I1bs/I1) because of the resultant reduction of the bow shock strength. Both the surface current density Jbs at the nose of the bow shock and the total bow shock current lb, share nearly the same relationship with MA, and vary non-monotonically with MA or Bs. The maximum point is found to be located at MA = 2.7. Three conclusions are then made as follows: (1) The surface current density at the nose, which is much easier to be evaluated, may be used to largely describe the behaviour of the bow shock instead of the total bow shock current. (2) The peak of the total bow shock current is reached at about MA = 2.7 when only Bs is adjusted. (3) The non-monotonic variation of the bow shock current with MA causes a similar variation of its contribution to region 1 FAC. The tuing point for such contribution is found to be nearly MA= 2. The implication of these conclusions to the saturation of the ionospheric transpolar potential is briefly discussed.