Out of pure curiosity: why would you want to shoot a bracket using ISO as your means to control exposure? Sony cameras are virtually ISO invariant (save for the second gain step), so raising ISO in camera or in post-production yields nearly identical results. Most people shoot bracketed exposures to gain detail in over- and underexposed areas, but when you use ISO as your exposure variable, you might as well just create the bracket in post by raising/dropping exposure. You don't gain any dynamic range that way.

That might be the problem.  My manuals specifically state to turn off STEADYSHOT when a tripod is used -- but it's easy to forget.  It's also easy to forget to turn it back ON when I remove the tripod!!!

The options for this technique vary from camera to camera.  For example, I can't do this at all on my cameras.  First, tell us what camera you are using, and second, tell us if you have a user manual.