If it is sunny enough for the bermuda to grow, there is no way you are keeping it out. If it is too shady for the bermuda to thrive, you don't need to to anything - the shade will do it for you.

When we plant "meadow/prairie" areas with Bermuda grass, we make sure to complete at least 2 grow kill cycles to prepare the soil. That involves making sure that everything is actively growing and spraying Roundup and spreading a pre-emergent. Bermuda grass produces an enormous amount of seeds if allowed to set. We let all that die and let a new round of weeds come up followed by another round of Roundup and pre-emergent. That is about all most people are willing to endure, although if I had my way I would complete another round. Each round takes about 3 weeks. Then we go in with native grass plugs leaving the ground untilled. If you till the area you will just expose more weed seeds. After about 6 months, the grass will be filling in nicely and you can heavily sow the wildflower seeds. There may be some bermuda grass that survives, but it is controllable by either roundup or digging it out. Just be careful with the spray. With these types of gardens, site preparation is incredibly important if you want to increase your chance of success.

sujiwan- I have some of that grass from hell, it's very hard to deal with. A black plastic barrier or weed fabric might suppress it over time, or it might find chinks to grow through. I think killing it out would be your best bet. A gc I have that is tougher than grass is ground cover Comfrey, Symphytum grandiflorum. I haven't tried it under roses, just under fruit trees. It gets around 6-12" tall. Vinca major once established is tougher than most grasses, though some can seed into it. It gets rather tall, though. Most of my other good gc lets grass grow up through it, so it's really hard to get rid of the grass- Vinca minor, Rubus calycinoides, Arctostaphylos uva-ursi, etc. Mulching really deeply to partially smother the grass and partially make it easier to pull out might help.

Tilling would have been the wrong thing to do, especially for bermuda, so don't hate on your installer. He did it right. Still the surface is not level. You can deal with that in December or wait until next June. The grass either needs to be completely dormant or growing like crazy. Your soil is not likely to be compacted. You can drive bulldozers over it all day long and it will not compact...unless the soil is saturated with water first. If the soil was saturated and then mechanically compressed, that would cause the particles of soil to squeeze the air out and that is the definition of compacted soil. Bricks are made of compacted clay. Adobe is made of compacted silt and sand. Almost no yards are truly compacted. However, many (MANY) yards are hard from a lack of adequate biology. New yards are especially prone to this because they don't get watered, fertilized with organics, and don't have a history of grass growing in them. Here's how to fix yours fast. ...and when I say fast, I mean in 3 weeks. Spray it with shampoo. Shampoo is a surfactant that will allow moisture to penetrate much deeper into the soil. When that happens the microbes in the soil have a more hospitable environment (cooler and moister) in which to thrive. It is the microbes that soften the soil for you. The shampoo application rate is 3 ounces per 1,000 square feet. If you have 3,000 square feet, put 9 ounces into a hose end sprayer, fill it with water, and try to spray it evenly until the sprayer bottle is empty. You can repeat this as often as you want to, but wait for 3 weeks before you decide to repeat. Before you spray it test the soil by pushing a screw driver into it. Do that before you water and after. Then spray the yard and apply a full 1/2 to 1 inch of water all at one time. You'll have to time how long to leave the sprinkler on yourself. Do that by placing cat food or tuna cans around the yard and time how long it takes to fill them. I can tell by looking at your (dry) yard that 25 minutes is not nearly long enough. Mine takes 8 hours with turbo oscillator sprinklers on a 3/4-inch hose. That time to water 1 inch is the time you should reset your sprinklers for. Once you know that number, reset the timer and set it to water only one day per week. Bermuda in Fresno should be able to handle one day a week watering easily. I just visited a St Augustine lawn in Phoenix that only gets water once a week, so you can do it with bermuda. When the soil is right it will be very soft when moist and very firm when dry. The shampoo treatment is a replacement for aerating. You won't have to aerate ever again. Use a clear shampoo like baby shampoo. Don't use one with conditioners in it. Cheapo shampoo is fine. Generally you are correct to use the highest nitrogen number you can get easily with zeros for the other numbers. You might want to spend $25 for a soil test at Logan Labs to see if you need P or K in your fertilizer. If you do that, post your results here on this forum. Morpheuspa will read it for you and tell you how much of anything you need to apply, when to apply, and where to buy it. In addition to monthly feeding with high N, I would urge you to add at least one app per year of any organic fertilizer. The organic fertilizers feed the soil microbes so that they can help you take care of the grass. For example they keep the soil from getting hard. They also feed the grass, and there are other benefits. You can apply organics at the same time you use chemical ferts, or any other day of the year. Have you tried mowing down to 1/2-inch and letting it come back up to 3/4? Do you actually hit the ground when you mow lower than 1 inch or does it just scalp off all the green and leave brown stems? Brown stems are normal until you get it down to the 1/2-inch range. If you mow it 3x per week at 1/2-inch it will start to grow horizontally like you see on putting greens at the golf course. That's often the objective for serious bermuda growers.