I don't think you will find a disposable diaper that is as thick as a cloth diaper. I have used the Secure X-Plus (they are made in the same factory as the Bambino, and for disposables, they are thick.) You definitely know you are wearing a diaper. If that's not enough, you can add baby diapers as stuffers, just cut slits into the plastic on the baby diapers, and lay them in until you are happy.
How tall are you and how much do you weigh?