As stated, salt will kill the Bermuda Grass. But the reason it kills the grass is because the salt is killing the life in the soil, including all beneficial bacteria
. In other words, adding salt to your soil is more or less the same as killing the soil, taking away it's ability to support life. Nuking the life out of your soil can harm its ability to support any life.
As Gary stated, the salt can be washed away, but it's not guaranteed. You cannot take it for granted the salt will be washed away. Your soil must have excellent drainage, AND you must be certain that you will have a significant amount of rain.
The heart of gardening is caring for your soil, encouraging it's health. I believe that killing your soil in order to eradicate one or two weeds can be considered an extreme solution that may do more harm than good.
A garden is a small spot on planet earth surrounded by billions of acres of good soil. It is a known fact after 10 rains the salt is gone. So what if everything in that small spot dies when salt is gone everything returns to normal like nothing happened every thing good migrates back into the spot and it returns to normal. It does not stay dead for ever. The highway department dumps Millions of TON of salt on highways and street all over the USA every year. Oil well salt water ponds will kill every thing in sight and it stays dead for as long as the salt water pond is there. When the salt pond is gone after several rains grass and weeds start to grow and soon the land returns to normal again. Salt is not a bid deal other wise EPA would have it listed in the same category as Agent Orange = 2,4,5,D.
I can show you 5 acres of land behind my Grandparents house in Fairfield Illinois where a salt water pond was that was deader that #$%^ for 30 years. After the oil well was closed and the pond bull dozed away that summer after several rains the whole 5 acres was covered in grass and weeds by the end of the summer. The very next summer my cousin planted corn were that salt water pond us to be. He has been planting corn there every year since 1980.
If you kill your garden with salt you better hope it rains about 10 times before it is time to plant your garden again. Snow melt counts as rain.
Potting soil is baked in an oven to kill everything including seeds. If you put potting soil in your garden soon all the micro organisms, worms and other thing migrate into the potting soil and soon it is full of grass and weeds. I does not take long for dead soil to return to normal all by itself.
Dead soil is a good thing just like a forest fire is good. Forest fire is natures way to get rid of the old to make room for the new.
I don't have a problem dumping salt on my yard. I killed all the wild onions in my yard with salt. I dumped about 1/4 cup of salt on each plant then waited for rain. Onion was dead so was a 6" circle of grass. One month later after a few rains the grass returned. It works.
We had a tree grow up next to the building at work. We cut that tree down many times but it kept growing back from the roots would could not dig up. Finally we dumped 150 of salt on the tree roots and it died.