a quick response for the time being:

How does the current Bermuda now? Unless you are wanting to start completely over, do not reeseed. Most likely you have Bermuda tiff. Even if you have a little, by this time next year, your yard will be looking 10x times better with proper maintenance. No Bermuda seed will match sodded Bermuda and will result in a weedy look.

Why do you think you need to aerate?

For the time being, google the Bermuda Bible. It will give you proper care techniques for Bermuda and may save you some time and money as far as trying to start over goes.

The aeration is because of the heavily compacted clay underneath the sod. Also there are bare spots where the sod didn't take. So I need to fix that.

Since your going to aerate, you can scoop up some of the cores and spread them in the bare spots. The cores have live grass and roots.......just tamp them down a little- topdress , and keep them wet like you would new seed.

in lieu of aerating, you can try search on here for the shampoo method. It will help with compacted soil. Aeration, if you do not have tools yourself to do it, can become expensive and also can disturb weed roots, resulting in numerous new weeds popping up in your lawn. Applying shampoo, can remember exact amount /sq ft. off hand, will help with the compaction. Search the forums and there are numerous posts explaining the benefit and how to apply.

As far as the bare spots, Bermuda will fill in pretty quick in those areas. If you can keep those areas moist (not soaked) through the day, the Bermuda will spread in even quicker.

Not trying to detour you from your plan, but just giving you options to consider.

I want to try to detour you from your plan. Something is wrong with the lawn and your plan will only make it worse.

Sodded bermuda is always Tiff 419 ($50 per pallet) unless you specify you want the expensive sports variety of Tiff ($250 per pallet). Tiff 419 is one of the best turf grasses you can get at any price. As it happens, growers found that out and went into massive production. The cost came down and now the best grass available is also know as "contractor's grade." As soon as you put common bermuda seed into that you will have a weedy looking lawn that cannot be restored to 100% Tiff without a full renovation. Even the so called hybrid seed is common bermuda, not hybrid Tiff. Tiff seed is not available.

So what's wrong with your lawn? My guess without seeing any pictures is you have trees, fencing, or buildings somewhere between the grass and the horizon. Bermuda needs a very full 6 hours of sunlight every day. If you have an open field with a brick mailbox that shades the grass, the grass will be thin and ugly on both the east and west sides of that mail box. Almost always when bermuda thins out it is due to shade issues. If that's your problem you need a different ground cover than bermuda. There is a variety of zoysia called Shadow Turf that will grow fine in the shade and can be mowed low like bermuda.

If your bermuda is not soft, you might be mowing it too high. If you are mowing less frequently than 2x per week, or if you are mowing higher than 1.5 inches, then mowing is the problem.

Are you deep watering 1 inch, all at one time, once every week.

Never top dress your lawn unless you have drainage issues, because top dressing will always lead to drainage issues. Some people swear by top dressing 1/4-inch of topsoil every year. Here's a picture of a house where they did that...for 40 years. The result is 10 extra inches of soil that leaks out into the street and sidewalk. These people fixed that but you get the idea.

Whatever reason you have for top dressing is not a good one...unless you have low spots that pool water when it rains. That is a good reason, but most people call that leveling and not top dressing.

If you suspect your soil is not perfect, there are two components to that: chemistry and biology. The biology is easy to fix with organic fertilizer. The chemistry is fairly easy to fix but you have to know exactly what's wrong. That requires a soil test. The best one, as you have likely read, is from Logan Labs ($25).

Post some pictures of your thin grass. Close up is good and some from a distance so we can see the surroundings. Lawn pix are best when taken on a cloudy day (ahem - I guess I couldn't wait for a cloudy day for the one I posted).

I have low spots and a slip in my back yard that leads to some draining issues. That is why I am wanting to leveling the yard. I sent a soul test off to Oklahoma State and I am waiting on the results. I do plan on using organic fertilizer to help out. I water 2 times a week trying to get a half inch in water depth per watering. Here are some photos. Ground is completely compacted. I did scalp the grass too much on the last mowing. Some spots look better than others.

Good post dchall...haven't seen that picture yet...I can't even begin to believe that whoever did that top dressing was thinking it was helping. Looks like the even had to put up edging next to the concrete to hold the soil in...wow!
I would like to add something that may not be clear...top dressing organic matter is ok...correct? Sand for leveling not topsoil right?