Mmmmm, very hard to explain. If I read you correctly you want the bounding box’s centre point to be in two different positions at the same time – you want the anchor point in the centre of the circle/image and at the same time for the bounding box to be centred in the composition so the image is off centre. As far as I know the centre of the bounding box is always going to be the centre of the bounding box. After Effects doesn’t see the circle/image as a separate entity, it only sees the whole 1080 x 1080 shape.
You are right, if the bounding box is at the exact edges of the image it will be centered, but that means that the image must fill the ‘canvas’ with no space around it – and it will import into the centre of your composition, which is not where you want it.
I’ll try to put my mind to an easy way of finding the exact centre of your circle/image but, no, there is no one click way of doing it – but I’m very happy to be contradicted by any of the clever people here.