It seems to me that the question of universalism—a challenge to the church's thinking for more than 18 centuries: in other words, nothing new—is not finally about doctrine or discrete beliefs per se, but rather two crucial second order tasks for the church.
The first is hermeneutics, which names the way in which the Christian community goes about reading the texts of Scripture, the "lens" or "guide" or "key" by and through which our reading attends to and accords with what the Spirit would have us hear as the word of the living Christ spoken to us today. Of course, this is a highly contested theological question, and there are no simple answers; the more important point, however, is that prior to engaging the texts themselves, there is open disagreement about how we should do that at all. Nor is the hermeneutical challenge answered by the texts, for they can only be interpreted as they are read, and that returns us to back again to how we shall read.
The second task is proclamation, having to do not with what is read or argued about or even taught within the church, but with what is spoken and declared publicly as the very word of the gospel for all to hear as good news. Here the Reformation principle of lex proclamandi lex credendi—"the law of proclaiming is the law of believing"—is especially helpful. Rather than ask, "What does the church believe about such-and-such?" the question becomes, "What should the church proclaim as gospel regarding such-and-such?"
Universalism challenges us hermeneutically by sending us back to texts we thought we already knew, urging re-readings and openness to others' voices, communal discernment and a softening of views which may have been self-interested or immovably rigid. And we enclose and surround that messy job of reading and re-reading with the charge of asking questions about the nature of Scripture, its use in God's purposes for the church, its relation to the content of faith, its diversity and unity and intertextual connections, and so on.
Regarding the specific question of universalism and the Bible, the issue seems rather straightforward: many texts clearly expect a final and decisive judgment by God on the wicked; many texts presuppose or assert that severe punishment will follow this judgment; many texts speak of eternality characterizing this judgment and/or punishment. At the same time, many texts speak without apparent reservation of universal or cosmos-inclusive salvation/redemption/deliverance, and those particular texts that speak of gehenna (hell) or haidos (Hades) contain enormous ambiguities related to genre, rhetoric, and historical referent.
Hence, how one "solves" the problem of salvation and damnation, and so answers the question of universalism, will have everything to do with hermeneutical decisions made prior to the interpretive act, specifically regarding the extent of biblical diversity and internal disagreement, the overall eschatological vision, the freedom of God over against Scripture, etc.
This is why Christians of different theological stripes belonging to different traditions of interpretation are bound to simply speak past each other in these sorts of conversation; the answer is already given in the way they approach Scripture in the first place. That is where the conversation must be had, instead of the (seemingly open, but in fact predetermined) doctrinal question.
And here is where the lex proclamandi comes in. Wonderfully, it cuts both ways, because in this case the universalist and the dual-destinationist will alike—assuming they believe what they believe because they believe it to be true—seek to proclaim, respectively, universal salvation or limited salvation. That is what Christians are called to do, after all: proclaim the good news to all as the truth of the final destiny of all things.
But perhaps there is another way. Indeed, I contend that Christians should proclaim neither universal nor limited salvation.
To refrain from preaching either doctrine has to do primarily with humility of language and respect for the tradition. On the one hand, I think it perfectly fine for a Christian to believe that all will be saved, or indeed, that all may ultimately be saved. But neither of these affirmations entails that the matter is settled, only that (at any one time or place) it is acceptable for a Christian individual or group to assent to them.
The essential logic is that, with regard to a question so ambiguous, contested, and ultimately unknowable, Christians should have the humility to halt their proclamation either way at the point of saying definitively whether all will be saved or some will be damned. The humility of faith demands it, for just as we should not claim to know without a doubt who is “out,” so also should we refuse the temptation to speak with absolute confidence on behalf of God concerning who is “in.” On what grounds would we make such claims, and for what reasons would we state them as public truth?
The negative rule of proclamation is, therefore, to preach the gospel in such a way that one never claims that any human beings will not be saved, nor that all human beings will eventually be saved. The positive rule is, vice versa, to preach the gospel in such a way, on the one hand, that all persons hear that they are rightly the recipients of the message of God's free and gratuitous good news, and, on the other hand, that one's response to this message is of decisive and eternal import.
The humility required, then, is first of all toward God: we must respect God's freedom as regards both the justice of divine judgment and the sovereign mercy revealed in Christ. After all, Scripture could be summarized as the story of God's successive overturnings of faithful believers' confident interpretations of prior, seemingly clear revelation. Should we not anticipate a similar upending of our own finite understanding, particularly concerning a question of such enormous weight?
Our humility is directed also toward the dead—that is, Christians from past ages. If God's freedom mitigates our arrogance to presume we have a "read" on others' final fate, here confidence in our own interpretation is qualified by those who have come before. For there can be no doubt that the destination of hell as a real possibility for some human beings dominates the church’s tradition (though there have been minority voices throughout); and in Scripture, too, while ambiguity is present, it is difficult to avoid passages about eternal punishment, burning fire, and final damnation. That does not mean we ought not to hope—or better, to pray—for the salvation of all, believing as we do that God desires all to be saved; only that it is neither our mission nor our prerogative to proclaim it to the world.