A bounding box, assuming it’s a sphere, contains two elements only: the center and the radius of the sphere. So for any given object, if you know these two elements, you have the bounding box.
Usually, (0, 0, 0) can be roughly seen as the center but you can take it serious – the center is a point where the vectors from each point to it sums up to zero vector.
As to the radius, it could roughly be defined as the largest magnitude of each components of each vertices (hence the making the minimum sphere to contain the object).
Once you have these two parameters, you can always tell whether two given objects are touching or intersecting by calculating the distance between the centers and comparing it to the sum of radii.