I do not know where is the bounding box of a Painter.
Looking at ApproximateQuadratic() and ApproximateCubic() it seems all painting shapes are reduced to lines stored in a LinearPathConsumer called rasterizer.
However I am lost when following Painter rendering process.
Well, from this reply I guess I was not specific enough. I do not mean all points of curve (or shape), but only those points you use to define it (3 points for quadratic, 4 for cubic).
Resulting bounding box would be larger than necessarry, but it might not be a problem in most cases.