When I flush the upstairs toilet a big bubble comes up in the toilet downstairs directly under the one just flushed.

That means you have a blockage in the main sewer line, after the downstairs toilet.

When water from the upstairs toilet is going down the main stack, it pushes the air in the stack out the downstairs toilet. The blockage is probably some distance away and is probably a partial blockage, otherwise you would have a backed up toilet downstairs.

Pull downstairs toilet and snake the line.