You could try giving the chickens a small amount and see how they take to the seeds. Easier to clean up a little than a lot. If it works, it's a great invention you made. Make sure the grass blades are not long, 'cause they can ball up in the chickens' crop and cause problems. I know from bad experience.

Just the grass clippings from the Bermuda grass are not a problem and you should be able to easily tell if there are any seed heads. At this time of year I would doubt that seeds would be a problem even in Bermuda grasses.

Guess I'm confused--How could seed heads NOT be a problem, if they go onto my fertile garden soil?

I think what kimmsr is saying, is that you can see the seed heads of Bermuda grass and know if they are present to be a problem. If there are seed heads on it, then you don't want to use the bags from that section of the yard on your fertile garden soil. Most people mow bermuda lawns before they manage to go to seed. However, around here bermuda is a common hay too.

Will the seeds still grow after them come outta the chicken again?

Grit in the chickens' gizzards will grind the seeds to a meal. Make sure the chickens have grit (finely crushed granite or other stone) available. Don't mistake crushed oyster shells for grit; it is a calcium supplement for egg layers and is too soft for grinding seeds.

Well, I dumped seeds and all in the garden, after thinking it over, what seeds make it thru the shredded leaves and grass to grow, should be easy to pull while they're tiny. another good idea suggested is to save several bags for the chickens mid-winter, to "sweeten" the house. And my chickens have access daytime to their acre lot, so stones for grit isnt a problem--lol--I;m in Missouri

First of all bermuda seed is the size of dust. If a chicken can eat that, it would take about 100,000 pecks to get a full gram of seed.

Secondly, I realize chickens are fed grains but it is my understanding that they prefer to eat meat protein. The diet you're suggesting sounds like a starvation diet.

Thirdly, you should not be collecting your mower's clippings. They should be left on the remaining grass as a source of nitrogen.

Finally, if you are mowing five acres, do you already have another 10 acres in fruit trees, rose gardens, statuary, pathways, patios, ponds, decks, hedges, arbors, gazebos, Japanese rock gardens, flower gardens (besides roses), trellises, picnic areas, barbecue facilities, and an outdoor theater? In my opinion there is not much less interesting than a huge expanse of uninterrupted grass.

My chickens have free choice egg pellets and corn, as well as about a fenced acre to catch bugs-just south of gardens.
And-I've left clippings lay on this for 42 years, I dont think this falls collecting is going to hurt.
and yes, the rest of the 40+ acres are in various things, including pastures and woods. this IS a farm, but thanks for the interest.
At this point, improving my garden beds seems the best choice, considering todays prices, having canned over 400 jars of produce helps out this year.