In the 1984 film version of Dune, as the Reverend Mother is dying, the Bene Gesserit finds Jessica with the Fremen and gets her to drink the water of life. How did they reach Arrakis, track her down and go to her without being seen by Harkonnen eyes?
I think you're confused, and the movie probably doesn't spell this out. The Reverend Mother on Dune did not belong to the Bene Gesserit, she was of the Fremen. The Bene Gesserit were not involved in this ritual at all.
While "Reverend Mother" is an official Bene Gesserit title bestowed upon a woman in the Bene Gesserit sisterhood who undergoes spice agony and changes the Water of Life to reach a higher level of awareness, the same title is also used similarly by other civilizations than the Bene Gesserit.
This is because the Bene Gesserit has seeded the galaxy with their myths to secretly spread their beliefs into seemingly unrelated religions, and gain footholds everywhere through a program called the Missionaria Protectiva, so it's not completely random.
The Fremen is one of those other civilizations that have their own non-Bene Gesserit Reverend Mothers. When the Fremen Reverend Mother, Ramallo, is near death in Dune, Jessica consumes the Water of Life to take over. (The fact that she was Bene Gesserit is inconsequential to her new status as a Reverend Mother here, although of course it made her an ideal choice to become the Fremen's new Reverend Mother.)
This is perhaps explained better in the book:
"There are several alternatives?" she [Jessica] asked.
"The Sayyadina," he [Stilgar] said. "Our Reverend Mother is old. " Their Reverend Mother!
Now I must probe this Reverend Mother mystery, she [Jessica] thought. And she said: "You spoke of your Reverend Mother … and I've heard words of legend and prophecy."
[…] In the sudden hush, Stilgar bowed to her. "Sayyadina," he said. "If the Shai-hulud grant, then you may yet pass within to become a Reverend Mother."
Pass within, she thought. An odd way of putting it. But the rest of it fitted into the cant well enough. And she felt a cynical bitterness at what she had done. Our Missionaria Protectiva seldom fails. A place was prepared for us in this wilderness. The prayer of the salat has carved out our hiding place. Now … I must play the part of Auliya, the Friend of God… Sayyadina to rogue peoples who've been so heavily imprinted with our Bene Gesserit soothsay they even call their chief priestesses Reverend Mothers.
Further reading on the Dune wikia: