LOL So first thing first: Bermuda lawns look like hell in March, the Sun rises in the East and that's just life.
When we bought our house 3 years ago we had the worst lawn on the block - scraggly bermuda with a ton of weeds and we bought around this time of year.
So... Here's what I did and would do:
1. Go get a gallon of the 20% Acetic acid vinegar from your local organic shop. Lowes has this in their organic section. Use a tank sprayer to spot treat the broadleaf stuff in your yard (including clover) BEFORE the Bermuda greens up (like now, hurry).
2. Mow low low low! Use the string trimmer too if you have to but take it down close to the ground. If you bag it, save it for the compost pile.
3. You'll want to spread some good organic fertilizer and you want to use some good soil, compost or the bagged composted manure from the store to level things out. Dips and holes make it hard to mow uniformly later. For a cheap, easy fertilizer in the lawn I like Milorganite (Lowes, Home Depot, Elsewhere) or the Gardenville 7-2-2. Milorganite has a lot of iron and will give you that DEEP dark green. It doesn't burn but it doesn't smell great at first.
4. Get a gallon of horticultural molasses: an ounce or two mixed with water and sprayed over the yard once per week for the next month will loosen the soil and get the fertilizer "digesting" so the plants can use it.
This is not as much work as it sounds like, I just killed your saturday basically but it's nice to get outside this time of year!
Next, if you have a lot of bare spots you will want some seed or plugs to fill it in but the way to get rid of weeds and have a perfect carpet of Bermuda is twofold.
1. Easy on the water! DO NOT sprinkle 15 minutes per day. Water it deeply WHEN IT IS DRY ONLY. This encourages deep roots and discourages disease
2. MOW MO! Don't mow it high once per week in April-June. Cut it LOW and keep it LOW even if that means twice per week. Every 3-4 days when it is growing well early in the year. This will make your lawn much more dense. If your grass is normally 4" high and you reach your hand in around the ground you'll see that there is an inch or so between grass plants. If you mow it down to 3/4" for a season then eventually there is no getting to the dirt - it grows so dense that it looks like carpet. In July and August you can take it up a bit once the temps get around 100 and stay there but take it back down in September. When you 'scalp' it, it looks like hell for a week or two but scalp, fertilize and water and you will have a great lawn deep into the fall.
One other thing I might try. There has been a lot of talk about a product called "THRIVE", not the one that's been around forever in the brown bottle but a new one - it inoculates your lawn with bacteria and fungus that are good for the lawn and help it feed. I've been experimenting with it this spring with good results.
If you want to drop by and chat sometime and see exactly what I do for different issues just PM me, always happy to help a newcomer figure this stuff out. Fortunately, it gets to be easier and LESS work intensive after a year because once everything is healthy, it pretty much figures out how to grow without much help
Here's my yard this week... OK, the winter rye is cheating I know but this yard hasn't seen any chemicals since I bought the house three years ago.