The most direct route is over the top to Petty France, Nailsworth, Stroud, and Brockworth, big hills though. I would personally favour a different route which is more miles, but flatter, and that is to follow the Avon down to Bristol, then cut across to the A38 and up through Gloucester to Chelt.
I hired a narrow boat about 10 years ago and went from Trowbridge to Bristol down the K&A canal, and then the Avon. It is a nice route, but there are parts you wouldn't be able to follow as there isn't a tow path. You can get on the sharpness canal tow path up to Glos if you want to do that if you did choose my alternative, and then choose the old Glos road between Glos and Chelt (I live in Chelt)