I think we're talking past each other here. An hour and a half from now, the bolt will still be in the vicinity of the ISS, but may semi-stabilize over time into the periodic relationship you've described, until drag deorbits it. Yes?
The four pieces, the bolt, the washer, the spring, and the ISS were in four different orbits instantly. The four orbits intersect at two points 45 minutes apart. The periods of the four orbits are similar but not exactly the same, so the four objects will come close to each other the first orbit and less close with each subsequent orbit.