It sounds a lot like the ponds that I fish. Usually they have water run off inlets from either parking lot run off or street run off. Mud bottoms with little to no cover and bowl shaped. No dam really just an out flow tube. 10-12 ft max in the middle and usually highly pressured.
One thing the ponds have around me usually have is boulders all the way around the pond for erosion control. A few trees around the edge here and there but nothing in the water as far as laydowns or brush piles.
The first thing i focus on is the banks. I start off fishing as close to the bank as possible early morning and late evening. The bass will move to the boulder banks and pick off the bait fish that are there feeding on the bugs coming off the rocks and out of the grass. I will throw shallow cranks and weightless worms or lizards. (top water can be fun as well. spooks,frogs,or my new favorite wake baits).
After a good hard rain the first place I am heading is the run off areas where the water is coming into the ponds. The bass will stack up there big time feeding on stuff washing in. You can throw just about anything in there and catch them when that is happening. Go to there is a weightless fluke or plastic swim bait. Also weight less t-rigged worms.
Mid day Focus on the deepest part of the pond. Throw a mid range 6-8 ft diving crank or 6-8 ft diving jerk bait. If there is a fountain or oxygen lines definitely hit them in the warmer months as it will stir up the water giving more oxygen(also usually the deepest part of the pond) Warmer months faster retrieves are better, cooler months slow as you can possibly go.
Google earth can be your best friend. You can roll back google earth a few years and see the different water levels. When I am looking at the older pictures I am focusing on the images when the water was the lowest looking for any variations in the bottom contour. Even if it looks like a dig out that is even a foot lower or higher than anything around it the fish will key in on that spot. Also look for any trees, stumps, logs, trash cans, anything that may look like structure.
Most of the ones I fish have about 2ft of visibility so I will throw natural colors, ghost colors and white colors up close to the bank and as i get deeper the darker the colors get.
Hopefully this helps you out a little bit. Tight lines and stick a good one.