Good afternoon, Rusty!
Yes, bourn or bourne can mean either a limit/ boundary, or a stream or dry chalk bed that can be flooded.
I have seen "The Quiet Man" - although many moons ago! Yes, an excellent film, altho my memory of the story is a bit dim......something to do with a dowry withheld by the heroine's brother?
I cannot remember where I was when I saw the film.......
If I recall correctly, Ward Bond - he of Wagon Train fame - was also in it?
The sun is still shining, the dog is getting restless....time to go out for a (quick) walk.