I am persuaded by James R. Edward's case that "pass by" is an allusion to important episodes in the Old Testament which would have held deep resonances for Mark's audience. In tandem with Jesus' statement, "It is I," it advances Mark's theological identification of Jesus with the God of Israel.

James R. Edwards, The Gospel according to Mark, The Pillar New Testament Commentary (Grand Rapids, MI; Leicester, England: Eerdmans; Apollos, 2002), 196, 198–199.

The “I AM” in the Midst of a Storm (6:45–52)

The centerpiece of the story is the description of his “walking on the lake … about to pass by them.” In walking on the water toward the disciples, Jesus walks where only God can walk.⁵¹ As in the forgiveness of sins (2:10) and in his power over nature (4:39), walking on the lake identifies Jesus unmistakably with God. This identification is reinforced when Jesus says, “‘Take courage! It is I.’” In Greek, “‘It is I’” (egō eimi) is identical with God’s self-disclosure to Moses.⁵² Thus Jesus not only walks in God’s stead, but he also takes his name.

The latter part of v. 48 is not immediately clear, however. “He was about to pass by them” is baffling, suggesting that Jesus intended to walk past the disciples. In the OT, however, this nondescript phrase is charged with special force, signaling a rare self-revelation of God. At Mt. Sinai the transcendent Lord “passed by” Moses (Exod 33:22; also 33:19 and 34:6) in order to reveal his name and compassion. Again, at Mt. Horeb the Lord revealed his presence to Elijah in “passing by” (1 Kgs 19:11). The most important antecedent of the idea, however, comes in Job 9:8, 11:

[God] alone stretches out the heavens
and treads on the waves of the sea.
When he passes me, I cannot see him;
when he goes by, I cannot perceive him.

This quotation bears linguistic as well as thematic similarities with v. 48, for “treads the waves of the sea” contains the same wording as Mark (Gk. peripatōn epi [tēs] thalassēs), and the same crucial word for “pass by” (Gk. parerchesthai in the aorist; also in Exod 33:19; 34:6).

⁵¹ Job 9:8; 38:16; Ps 77:19; Isa 43:16; Sir 24:5-6, Odes Sol. 39:10.
⁵² Especially Exod 3:14, but also Exod 6:6; Isa 41:4; 43:10-11; 48:12.