Just how densely packed do you think asteroid belts really are? Are you using the (((hollyweird))) sci-fi space movie depictions as your basis for just how much stuff there is in an asteroid belt? Much like the satellites orbiting Earth, there is an incredible amount of space between significantly sized objects in the belt. Even in planetary ring systems there are huge swaths of emptiness between the significant chunks of ring material. It's not jam packed with rocks. It's safe to traverse the belts because there's just not that much in the way.