Assuming a ball bearing is perfectly spherical, and it is placed on a perfectly flat steel plate...?

A ball bearing is just kept on a Perfectly Flat Steel Plate, the bearing wont indent any bit into the plate. Contact between two bodies is of two types- Surface Contact and Point Contact .

Here, the contact will not be a surface contact rather a Point Contact.

So, there's no surface area to measure..

or if you are die hard to find out the area of that point, then use magnifiers and get its radius and do [pie]r^2 -[don't do it though]

Theoretically it would just be a point, but in practice it will be more than that.