Bermuda grows in cracks in the street and such, so you should be able to grow it. Make sure the soil ph isan't too high , and its well fed with organic fertilizers.

I dont have very rocky soil but have very thick clay and notice in the hottest/dryest months my bermuda doesnt look as green. I too cant get a screwdriver to go all the way, especially in the dryer hot months. So next spring I plan on doing some aerating, Something I have never done. My local rental place rents them for $50 per day. I hear its a workout doing it yourself, Especailly if you have hills like I do.

My advice is stay on a yearly aerating schedule(In the spring every year for bermuda).

Theres this guy on youtube who purchased an aerator for himself and he does it 3 times a year now and you can see a HUGE difference in his lawn.

Also it wouldnt hurt to do a soil test.I did my first one ever a month ago. Soil savy at amazon is the one I purchased. My PH was perfect but it showed my soil was very low on phosphorous and potassium.

Yes, that's what the home landscape people do around here when they're putting in a subdivision. They throw a few inches of soil on caliche, and call it a lawn. The simplest thing to do is to get used to a brown lawn in the deep summer. The roots will be fine, and green up in the spring. Making it green through the summer is going to be painful and expensive.

Trees are far more tolerant of the layer of rocks under the soil than is turf grass. Their roots are pretty expeditious in finding cracks between them. I've planted oaks on a few inches of soil (with an excavated hole large enough for the root ball), and they do great. In fact, that's exactly how they propagate naturally. They'll grow where the acorn falls, and not where the soil is deep.