Polyphant is correct, it can operate either way. It's hypothesized that Jupiter in 2:1 resonance with Saturn was the cause of the late heavy bombardment. Source
The 2 largest objects in the solar system operating in resonance tended to stir everything up. Many small objects including Neptune and Uranus were thrown around, some into the sun, some in towards the inner solar-system where some crashed into other planets and some out of the solar system or into the Kuiper belt, but all that ended 3.8 billion years ago.
The dummies answer is that most of the stuff in the solar system that had orbits that were likely to crash into a planet have already done so, and Jupiter sped that process up.
The slightly longer answer follows:
For the time being, the asteroid belt is mostly stable, as are Jupiter's two Trojan regions, L4 and L5 and Jupiter's hildas are also stable. So that's basically why we're in a low bombardment period now. The inner solar-system objects are mostly in stable orbits where they aren't in position to crash into planets. To collide, orbits need to cross and mostly the inner solar system objects don't cross orbits with planets.
Computer simulations suggest that the original asteroid belt may have
contained mass equivalent to the Earth. Primarily because of
gravitational perturbations, most of the material was ejected from the
belt a million years after its formation, leaving behind less than
0.1% of the original mass. Since then, the size distribution of the asteroid belt is believed to have remained relatively stable.
Similarly, Jupiter Trojan objects, L4 and L5 and Jupiter Hildas are in mostly stable orbits due to the high mass of Jupiter, so it's a two fold answer. First is that late heavy bombardment removed most of the inner solar system objects that were bombardment candidates, and 2nd, the huge mass of Jupiter compared to the inner planets and the significant relative distance between Jupiter and Mars and the small mass of Mars), together creates a healthy amount of relatively stable orbital regions where asteroids can stay in stable orbit and not be in position to crash into the 4 inner planets or be subject to n-body instability of multiple body orbital systems. (I can add various articles on the stability of Jupiter's L4 and L5 and Hildas, but they're not hard to google).
For Kuiper belt objects, I don't believe Jupiter has much of an effect pro or con, for earth impacts, though it blocks a few of those, but it should only be a small percentage, but I suspect Kuiper belt object collisions with inner planets are less frequent. For inner solar system objects (asteroid belt, L4, L5 & Hildas), that's where Jupiter significantly reduces impacts with inner planets, for most of the last 3.8 billion years.
A curious sidebar is that Jupiter may, at some point in the future, stir things up in the solar-system again and create another much smaller heavy bombardment period. This would depend on the Jupiter-Mercury resonance and if Jupiter was able to pull Mercury away from the sun, as some models suggest it might.
This is low probability and if it happens it won't happen for billions of years, but if Jupiter does cause Mercury to migrate away from the sun, Mercury passing through the asteroid belt, hildas and L4 or L5 would likely cause a significant increase in bombardment.
This article doesn't mention the asteroid factor, but Mercury passing through any of the asteroid rich regions of the inner solar-system would stir things up quite a bit and significantly increase the chance of bombardment.