Bad back can mean a whole lot of things. At 65 I am guessing you want to ride for health reasons. You're going to come to grips with the normal aches and pains of any exercise activity and bike riding will have them. Don't allow that to discourage you. The release of endorphines from bike riding will get you to a level of aerobic fitness that will make you feel 10 years younger.
In your corner, get a good professional bike fitter. Good fitters know a lot about aches and pains. Good fitters do like a history and physical evaluation first. Its unfortunate that bike fitters aren't covered by Medicare. Maybe we can get AARP to lobby for it.
Biking is a means and not and end. As a kid I never had a geared bike. So drop the "dumbrailer" talk.