The same Rufus may have been mentioned in Polycarp's Epistle to the Philippians (ch. 9):
Παρακαλῶ οὖν πάντας ὑμᾶς, πειθαρχεῖν τῷ λόγῳ τῆς δικαιοσύνης καὶ
ἀσκεῖν πᾶσαν ὑπομονήν, ἣν καὶ εἴδατε κατ’ ὀφθαλμοὺς οὐ μόνον ἐν τοῖς
μακαρίοις Ἰγνατίῳ καὶ Ζωσίμῳ καὶ ῾Ρούφῳ, ἀλλὰ καὶ ἐν ἄλλοις τοῖς ἐξ
ὑμῶν καὶ ἐν αὐτῷ Παύλῳ καὶ τοῖς λοιποις ἀποστόλοις
I exhort you all, therefore, to yield obedience to the word of
righteousness, and to exercise all patience, such as ye have seen
[set] before your eyes, not only in the case of the blessed Ignatius,
and Zosimus, and Rufus, but also in others among yourselves, and in
Paul himself, and the rest of the apostles.
Pseudo-Hippolytus enumerates Rufus as one of the Seventy Apostles (Luke 10), and lists him as "Bishop of Thebes".
Rufus is in commemorated in the Synaxarion of the Eastern Orthodox Church on April 8. An entry in the Synaxarion of the Monastery of Simonos Petra on Mt. Athos (Greece) states:
Saint Rufus may have been the son of Simon of Cyrene mentioned in
Mark's Gospel (15:21). In his Epistle to the Romans, Saint Paul
writes: Salute Rufus, chosen in the Lord, and his mother and mine
(16:13). He later became Bishop of Thebes, in Greece.
The Synaxarion: The Lives of the Saints of the Orthodox Church,
Vol. 4 (March-April), p.371
This, of course, is a modern work, but the Simonas Petras compilation is derived from a long stream of written tradition on Mt. Athos that dates back to at least 800 AD.
The latter Great Collection of The Lives of the Saints, by the Russian Sergius of Radonezh (d.1392) does not mention the connection with the Rufus of Mark, nor does Nikolai Velimirovic' Prologue. These latter two, along with the Simonas Petra volumes, are the most comprehensive Synaxaria that have been translated into English, so from an Orthodox Christian perspective the best one could say is that the connection with the Rufus of Mark is tentative.