Before we get into the weeds, here are the main points that I intend to impart:
Reformed theology generally accepts the church fathers' wisdom on the homoousion.
The concept of homoousion, not the term, is what matters most.
The concept of homoousion safeguards the Gospel against Arianism.
There is no single proof-text for the term, but the concept is inseparable from the Biblical witness.
And now we move into the weeds.
Francis Turretin, author of one of the classic reformed systematic theologies, affirmed that the church father Basil was correct to advance the term despite a lack of singular proof-texts:
Francis Turretin [Institutes of Elenctic Theology, 1:37-39] asked whether Christian doctrine was to be legitimately proved "only by the express word of God" or also from "consequences drawn from Scripture." He observed that "a thing may be said to be in Scripture in two ways: either kata lexin (expressly and in so many words); or kata dianoian (implicitly and as to the sense." It is unnecessarily reductionist to suggest that a doctrine is biblical only if a proof text can be adduced. Turretin drew attention to Basil's response to the Arians in which he argued that their demand for a proof text to establish the homoousion rendered them "syllable-catchers."
Mark D. Thompson, "The Divine Investment of Truth," in Do Historical Matters Matter to Faith, 75
The church father Athanasius believed that the concept has its origin in the New Testament:
Athanasius ... rightly recognized that the proper understanding of the homoousion was lodged within the New Testament from the outset. The homoousion may be a word foreign to the New Testament, but it was, ultimately, not a concept foreign to the New Testament, for the New Testament proclamation did not simply give rise to it but actually contained its meaning.
Thomas Weinandy, Athanasius: A Theological Introduction, 136
For Athanasius, the entire Gospel was at stake in the debate against Arianism:
It must be stressed that so far as Athanasius was concerned it was not the word homoousios itself that was of central importance, but what the word stood for. There was no substantial change in his position when he came more and more to use homoousios in his writings: it served simply to focus and concentrate the entire debate with Arianism. What it meant for Athanasius was simply this: that the reality of God himself is present with us and for us in Christ. "One ousia" means "one divinity", "one activity", "one presence", "one glory", "one power and energy": all that the Father is, the Son is also, except that the Father is Father, the Son, Son. This was the decisive difference between Athanasius and Arianism; for any assertion of this kind was, in the Arian horizon, strictly incorrect and untrue. For Arius and his followers, however, the point might be expressed, decorated or qualified, the Son is not God as the Father is God; for Athanasius, he is.
[From Athanasius' perspective,] what was missing in Arius' entire scheme was, quite simply, God himself. True, he was there—after a fashion. He was there, but he was silent, remote in the infinity of his utter transcendence, acting only through the intermediacy of the Son or Word, between whose being and his own, Arius drew such a sharp distinction. The God in whom Arius believed had no direct contact with his creation; he was for ever and by definition insulated and isolated from it in the absolute serenity of an unchanging and unmoving perfection. God himself neither creates nor redeems it; he is involved with it only at second hand. This is on the one hand the corner-stone of Arius' theology, and on the other the point of fundamental contrast with Athanasius. This remote transcendence, Athanasius rightly sees, has nothing to do with the God of the Old and New Testaments, the Father of Christ. When Arius' system is put to question, not simply about its own internal logic, but about its adequacy as a means of interpreting and expressing the Gospel, it is found to be hopelessly inadequate; for the Bible speaks of a God who is present and who does act in and for the world which in his own, and whose presence and activity are uniquely concentrated in the man Jesus who is at the same time Immanuel, God-with-us. For Arius, that cannot really be; for Athanasius, it is the centre around which everything else falls into place.
Alasdair I.C. Heron, "Homoousios with the Father," in The Incarnation, 68-69
Here's an example of Athanasius' scriptural reasoning at work in the homoousion controversy:
The bishops ... were again compelled on their part to collect the sense of the Scriptures, and to re-say and re-write what they had said before, more distinctly still, namely, that the Son is 'one in essence' with the Father: by way of signifying, that the Son was from the Father, and not merely like, but the same in likeness, and of showing that the Son's likeness and unalterableness was different from such copy of the same as is ascribed to us, which we acquire from virtue on the ground of observance of the commandments. For bodies which are like each other may be separated and become at distances from each other, as are human sons relatively to their parents (as it is written concerning Adam and Seth, who was begotten of him that he was like him after his own pattern); but since the generation of the Son from the Father is not according to the nature of men, and not only like, but also inseparable from the essence of the Father, and He and the Father are one, as He has said Himself [John 10:30], and the Word is ever in the Father and the Father in the Word [John 10:38], as the radiance stands towards the light (for this the phrase itself indicates), therefore the Council, as understanding this, suitably wrote 'one in essence,' that they might both defeat the perverseness of the heretics, and show that the Word was other than originated things. ... If the Son is Word, Wisdom, Image of the Father, Radiance, He must in all reason be One in essence.
Athanasius, De Decretis, 20,23
Lastly, observe how reformed theologian Stephen J. Nichols affirms each of the main points listed above while citing additional verses for reference:
The bishops at Nicea concluded that homoousios alone measured up to the standard of biblical teaching. The Nicene Creed declares that Jesus is "very God of very God, begotten not made, being of one substance with the Father."
This creed is not uncovering new ground. Rather, it summarizes the massive swath of biblical material regarding the person of Christ. The author of Hebrews begins by declaring, "He is the radiance of the glory of God and the exact imprint of his nature" (Heb. 1:3). Paul says rather directly that in Jesus "dwells the whole fullness of deity bodily" (Col. 2:9).
The Nicene Creed is a prime example of systematic theology at its best. Systematic theology seeks to organize and summarize, not add or detract from, the biblical teaching. Systematic theologians then teach this doctrine to the church. These bishops in the early churches were systematic theologians. The creed the bishops constructed at Nicea was their gift to the church.
Stephen Nichols, "Christology in Context," Tabletalk Magazine (12/1/14)