Check if bounds is Encapsulated in another bounds

static bool BoundsIsEncapsulated(Bounds Encapsulator, Bounds Encapsulating)
{
    return Encapsulator.Contains(Encapsulating.min) && Encapsulator.Contains(Encapsulating.max);
}

To extend the answer, you can extend the Bounds class to add a ContainBounds method

 public static class Boundsxtension
 {
     public static bool ContainBounds(this Bounds bounds, Bounds target)
     {
         return bounds.Contains(target.min) && bounds.Contains(target.max);
     }
 }