Trying To Get Rid Of Bermuda Grass

I have one main problem in my yard- Bermuda grass.  We bought our house brand new.  So when we did buy it there was no sod in the back yard.  I liked that we had a clean slate and I was able to design the yard the way I wanted it to look.  No problems there.  When we got around to adding grass to the back yard we spent about $2,200 on St. Augustine grass.  I thought at that price we were getting good grass but there was plenty of Bermuda grass that came with the St. Augustine.  It has now been about 9 years that we have had our house and the Bermuda grass has made its way into my flower beds.  It is literally taking over and I am so tired of digging it out that I am on the verge of getting Round up.  Really I wouldn't buy that stuff.  Round-up is horrible and I have recently read that they are now finding Round-up residue where it has never been sprayed before and also in the air.  Did I say how bad Round-up is?
So I am now trying to find ways to organically get rid of it for good.  The one thing that I have not got around to is making a 3-4 inch dead space (just dirt space) between the flower bed edging and the grass itself.  So I will need to get to that soon.  After that I will put a barrier deep in the ground at the edging so I can hopefully stop the Bermuda grass from coming in the flowers beds in the future.  Then the next thing I will do is spray vinegar on the Bermuda grass without getting it on the other plants.  I am going to try this at the hottest part of the day.  Since I have a background in Horticulture I do know that the vinegar will only kill the top of the plant and not translocate to the roots of the plant.  So I intend to do multiple sprayings of vinegar.  I am going to experiment with this and find out what type of spray schedule is going to work best.
So far I really have no idea if this is going to work but at this point I am willing to try it because I don't want to have to dig up this plant any more.  Wish me luck.