Here is what Köstenberger put in his commentary:
The reference to the physical setting of this event serves as a structural link indicating the end of the paragraph (cf. 6:59; 8:20; 11:54). It also helps transition to the climax of John’s testimony in the ensuing verses (Ridderbos 1997: 68). John takes care to distinguish this “Bethany beyond the Jordan” (cf. 10:40) from “Bethany near Jerusalem,” the village where Lazarus was raised from the dead (11:1, 18).
The Bethany mentioned in the present passage, which was one of the places where John baptized (note the later reference to Aenon near Salim in 3:23), is probably not a village but the region of Batanea in the northeast (called Bashan in the OT; see Carson 1991: 147; followed by Keener 2003: 450; Witherington 1995: 66). This is suggested by the fact that Jesus is said to leave from Bethany for Galilee in 1:43 and apparently calls Philip to follow him still on the same day. Hence, Bethany must have been within a day’s journey, and thus closer to Galilee than to Judea.
If this reconstruction is correct, then “Bethany” would be a variant spelling of “Batanea” chosen by the evangelist to underscore that Jesus’ ministry began and ended in “Bethany.” At Bethany in the (Galilean) north, John the Baptist confesses Jesus as “God’s lamb”; at Bethany in the (Judean) south, Jesus nears his crucifixion. The mention of all four major regions of the promised land—Judea, Samaria, Galilee, and the p 66 Transjordan (of which Batanea was a part)—indicates that the sending of Jesus is for the whole of Israel.
Andreas J. Köstenberger, John, Baker Exegetical Commentary on the New Testament (Grand Rapids, MI: Baker Academic, 2004), 65.
D.A. Carson suggests the same in his commentary:
The Bethany most commonly mentioned in the Gospels lies a short distance east and slightly south of Jerusalem, on the road to Jericho, and is best known as the home of Jesus’ friends, Mary, Martha and Lazarus (11:1). The Bethany mentioned here, however, is located on the other side of the Jordan, from the vantage point of the western side. Because there is no known Bethany on the east bank, numerous theories have been advanced. Some adopt the reading ‘Bethabara’—a known village but almost certainly not the original text. Apart from the textual evidence, which strongly supports ‘Bethany’, John takes equal pains to identify the other Bethany’s proximity to Jerusalem (11:18), which suggests that in his own mind he is referring to two places with the same name.
Although a dozen other suggestions have been advanced, recent research indicates that the most plausible theory is that the text refers to p 147 Batanea (called Bashan in the Old Testament), not a town or village but an area in the north-east of the country, to which Jesus himself withdrew toward the end of his ministry when opponents in Judea were trying to kill him (10:39–40). This is more likely than any site in the tetrarchy of Herod Antipas, since by the end of Jesus’ ministry Herod had already executed John the Baptist and generally ruled with more paranoia and cruelty than did his easy-going relative Philip, who ruled over Batanea.
D. A. Carson, The Gospel according to John, The Pillar New Testament Commentary (Leicester, England; Grand Rapids, MI: Inter-Varsity Press; W.B. Eerdmans, 1991), 146–147
Borchert suggests it is impossible to know for sure where the spot was located:
The pericope concludes with a notation that the event occurred at Bethany beyond the Jordan. This Bethany is not to be confused with the village of Lazarus (11:1), which has traditionally been viewed as situated just over the brow of the Mount of Olives near Jerusalem. No substantive evidence has yet come to light concerning a Bethany where John could have been baptizing (1:28).
The ancient map at Madaba shows Betharba (“the place of crossing”), and some have suggested it might refer to “the place of the ship.” Since Origen was familiar with the area in his day and could not find a Bethany, he chose to identify the place with Betharba. It is perhaps best to assume that it probably was not a populated area and its location has thus not been preserved in the designations of any villages or sites known today
Gerald L. Borchert, John 1–11, vol. 25A, The New American Commentary (Nashville: Broadman & Holman Publishers, 1996), 133.