Irv,,,,,I've got a Swift 8-32x50 on my 243 Ultra with plenty of hammer space with the same rings you're planning on using. But then my 223 Handi also with a Swift 4-12x40 and the same rings,,I needed to grind a bit off the hammer to get a millimeter clearance.
So it may be the placement and the build of the Bushnell for your personal eye relief as to whether you have clearance or not.