I agree with @mbloch that it seems logical that Rabbi Eliezer and Rabbi Yehoshua simply did not return to Yerushalayim after they assisted Rabban Yochanan ben Zakkai's escape. I think the story's main focus is RYBZ and how he created the new Jewish center in Yavneh, and wasn't intended to discuss the particular details of how each of the other sages survived. There are, in fact, some alternate versions of their escape. One version mentions the other prominent students of RYBZ together with Rabbi Yehoshua and Rabbi Eliezer (Avot de-Rabbi Natan version B, 29). Another version mentions Rabbi Tarfon or Rabbi Akiva (only the first letter of the name was preserved; unclear if it's a ט or an ע) lamenting RYBZ as part of the funerary procession (Genizah fragment, shelfmark JTS: ENA 3843.15).
The exact details of how each survivor of the Churban escaped Yerushalayim remain a mystery. Of course we know much of RYBZ's story. There are hints that other sages and their families survived harrowing events. For example, in Mishna Ketubot 2:9, Rabbi Zechariah ben Haktzav recounted:
"I swear by this abode of the Divine Presence that my wife’s hand did not move from my hand from the time that the gentiles entered Jerusalem until they left, and I know for a fact that she was not defiled. The Sages said to him: A person cannot testify about himself. The legal status of one’s wife is like his own status in this regard. Therefore, your testimony is not accepted, and your wife is forbidden to you."
But in most cases, we don't know how exactly sages survived the Churban and escaped Yerushalayim.
What we do know is that not long after the Churban, several sages and even some of their family members popped up in various cities and towns mainly around Judea but also around the Galilee and elsewhere. In the case of Rabbi Yehoshua, he settled in Peki'in (פקיעין) (Sanhedrin 32b; Tosefta Sotah 7:6), and once visited his rabbi, RYBZ, in Bror Chayil (Tosefta Maaserot 2:2/Yerushalmi Demai 3:1).1 Rabbi Eliezer, on the other hand, went to live in Lod together with his wife Imma Shalom and his brother-in-law, Rabban Gamliel II (e.g., Sanhedrin 32b; Tosefta Maaser Sheni 5:16; Tosefta Pesachim 3:11). After RYBZ's term as Nasi ended, Rabban Gamliel moved to Yavneh (sources), and it seems that Rabbi Eliezer and Rabbi Yehoshua spent at least some of their time there (e.g. Sanhedrin 17b). From the sources we have it's apparent that both students of RYBZ remained on good terms with their rabbi. As to why they did not live in Yavneh with him, one can only guess.2
1 RYBZ is said to have moved to Bror Chayil sometime after the destruction (Sanhedrin 32b). Most are of the opinion that he moved there after Yavneh. My personal view, is that Bror Chayil is another name for Yavneh and its vicinity.
2 My personal view (based on many sources which I will not get into here) is that RYBZ implemented a decentralized leadership model, which necessitated spreading the sages all over the Land of Israel. Rabban Gamliel, on the other hand, implemented a centralized leadership model, which demanded bringing most of the sages to Yavneh.