Neither the text nor any other writing of Tolkien I've been able to find supports or denies any hypothesis about whether the Rangers accompanied Gandalf and the hobbits to Rivendell but not beyond, to Rivendell and part way but not all the way to Bree, or not at all. At best, the hypothesis is weakly denied (that is, denied by omission of any positive reference).
First, let's start at the beginning of the journey, with those who were in Théoden's funeral procession from Minas Tirith to Edoras. In addition to the people you mention, there are also
- Faramir ("the Prince of Ithilien")
- Imrahil ("the Prince of Dol Amroth")
- "Many captains and knights" (apparently of Gondor, with whom Pippin rides)
- Éomer (whom you do mention; but Éowyn, whom you also mention, is not present)
- "An éored of the fairest knights of the Mark" [i.e. of Rohan], who had accompanied Éomer from Rohan
- The "folk" of Galadriel and Celeborn, seemingly Silvan or Sindarin elves from Lórien
- The people of Rivendell, referred to directly after Théoden's funeral, who apparently include "Glorfindel, Erestor, and the whole household of Elrond," who had accompanied him from Rivendell in the previous chapter
Importantly, not all these are named characters; there are three groups which are mentioned, but not named person by person; and the Rangers are not among them. It seems reasonable to believe, though far from certain, that if the Rangers had been in the funeral procession, they (like the captains and knights of Gondor, and the people of Lórien and Rivendell) would have been mentioned.
I see four possible conclusions:
- The Rangers were not in this group after all, but left at some other time.
- The Rangers were with the funeral procession, but for some reason are the only ones not listed by the narrator.
- Tolkien intended to list the Rangers, but overlooked it both in the first edition and in subsequent ones.
- The Rangers were with the funeral procession, and counted among some other group, such as the "knights and captains".
One might speculate about which of these seems most reasonable; but none of the options is either explicitly supported or explicitly denied by the text.
Next consider the other end of the journey, in Bree. There's no mention of the Rangers coming to Bree; indeed the description of the arrival at Bree specifically states:
So it was that near the end of a wild and wet evening in the last days of October the five travellers rode up the climbing road and came to the South-gate of Bree.
(The Return of the King, Book VI, Chapter 7, "Homeward Bound"; emphasis added)
It is certainly possible, one supposes, that the Rangers did accompany Gandalf and the hobbits earlier and simply "faded away" to take positions outside Bree before the "main party" arrived there. But that seems unlikely; Chapter 6, in the description of the departure from Rivendell, states
The next day Gandalf and the hobbits took leave of Bilbo in his room, for it was cold out of doors; and then they said farewell to Elrond and all his household.
This certainly seems to imply that it was only Gandalf and the hobbits who traveled from Rivendell; and the beginning of Chapter 7 reinforces this by saying that
At last the hobbits had their faces turned towards home
(though this does certainly discount Gandalf).
Although it is therefore a possibility that the Rangers accompanied the hobbits and Gandalf partway back from Rivendell, there's no textual evidence to support this; and as I interpret it there is at least some evidence (this last line) against it.
Further than that, there's no support for any particular position. All we know is that
- The Rangers are not specifically mentioned after the Battle of the Pelennor Fields.
- In particular, the Rangers are not listed as leaving Minas Tirith with Gandalf and the hobbits.
- The narrator specifically says that only the hobbits and Gandalf arrived at Bree.
- Gandalf states that the Rangers "came back with" them; but one could at least imagine some other interpretation of the phrase besides the most apparent.
That's all we get.