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.
Bambinos are good, Secure X-plus is just a bit thicker. I've been told that Dry 24/7 are amazing. However, if you want something really really thick try Abena Abri Form X-plus with an Abena Abri-let Maxi booster. You should be able to get smaples of both online from xp medical. This is without a doubt, the thickest setup you'll get. You won't be sorry