The four wire run was correct, as the outside disconnect becomes your main, and the panel inside is technically a sub panel. Someone didn't know what they were doing. All of the neutrals belong on one bar, all of the grounds on another, the two bars are most likely strapped together somewhere, probably at the bottom, and this connecting strap should be removed. The ground bar should have a green screw run thru it to the back wall of the panel or have a short ground strap from it to the back wall of the panel. The neutral needs to be electrically isolated from the metal housing of the panel.
The bar on the bottom is the ground, it has the smaller lug, where that bare ground should be connected. Separate the bars electrically and make sure the neutral is isolated and the ground is bonded to the can. Any neutrals on the ground bar need to be re-routed to the proper neutral bar (wirenut and more wire works if needed), and same for grounds on the neutral bar, extend or re-route them to the ground bar.