How much shade is that area getting? How often do you mow and at what length?

Shade or pH problem. Have you had a soil test or checked pH? All the fert in the world won't help in that case.

What is the best way to check the Ph or who can do it

I would top dress If possible rent a top dressing spreader. The more I look at your photo I would buy some sod and cut some 3x3 cores plant them in a Checker board pattern along with the top dressing and I would do it now.

This is good enough. I had applied lime to this area a couple of months ago, so its looking slightly alkaline. The rest of my turf is more neutral.

http://www.amazon.com/Luster-Leaf-1612-Rapitest-Tester/dp/B0001LEPYA/ref=sr_1_4?ie=UTF8&qid=1370184861&sr=8-4&keywords=ph+meter

If you use a store bought pH tester, be sure not to use tap water. My tap water has a pH of about 8.

Where do you live? I suspect your soil has not warmed up enough for the bermuda yet. Too many clouds and rain. Top dressing often gives the effect of stimulating new growth when actually it was the warming of the soil over time that stimulated the new growth. Adding topdressing will always change your drainage so you must be very careful. Here is a picture of a lawn where they have topdressed with 1/8-inch of topsoil routinely over the past 80 years. As you can see, it builds up to the point where they had to install landscape barriers to keep the soil from washing out onto the sidewalk - and still they keep adding more every year. Seems crazy to me.

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They have something like 18 inches too much soil there. Maybe when they bury the stop sign they will stop with the topdressing.

If you want a good soil test, Logan Labs in Ohio is the gold standard for lawns. Their $20 test gives as much information as a $100+ test from anywhere else. The $20 test from your local county extension service are usually unreliable and do not tell you all about your micro nutrients needed to perfect your soil. The Logan Labs tests are in continual reliability test mode on another forum where they specialize in reading soil tests from around the country.

Good point Dave. I used bottled water. I routinely (annually) use Logan Labs. I use the handy dandy little tester for localized checks where it looks like the turf is having trouble repairing.