First, Iain Murray has the following note in his book:
C. P. Venema writing on 'Heinrich Bullinger's Correspondence on Calvin's Doctrine of Predestination, 1551-1553,' says that while Bullinger rejected Melanchthon's synergism, he taught: (1) that the apostles 'understood God to desire well of all men,' wanting all to be saved and to come to the knowledge of the truth; (2) that 'those who perish do not perish by virtue of being compelled by a fatal necessity, but because they willingly reject the grace of God'; (3) that those who are saved are saved by 'the mere grace of God,' understanding faith to be his gift. (The Sixteenth Century Journal XVII, 1986), pp. 439–42.
Here are some relevant quotes from Venema's article that Murray references:
In any case, Bullinger [in his personal letter to Calvin] pointed to his teaching in the Decades where he had shown that God is a "friend of man" (philanthropos) who, because of his mercy, "wants all men to be saved" (vult omnes homines salvos facere).Cornelis P. Venema, "Heinrich Bullinger's Correspondence on Calvin's Doctrine of Predestination, 1551–1553," in The Sixteenth Century Journal 17.4 (Winter 1986): 439.
Venema quoted Bullinger directly as saying this as well:
Therefore, however many men are preserved, they are preserved by the mere grace of God the savior; those who perish do not perish by virtue of being compelled by a fatal necessity, but because they willingly reject the grace of God. Indeed, there is no sin in God; both this and the blame for damnation inheres in us.22Ibid., 439–440.
22. CO 14:208: "Quotquot ergo homines servantur mera Dei servatoris gratia servantur: qui pereunt, non fatali necessitate adacti pereunt, sed quod volentes gratiam Dei respuerent. Neque enim peccatum in Deo ullum: in nobis id et culpa damnationis nostrae inhaeret."
To this letter Bullinger appended a series of aphorismi de praedestinatione, in which he cited fourteen passages on salvation and damnation from the Consensus Tigurinus. With respect to election, Bullinger wrote:Ibid., 440–441.
God the father who is a friend of all, and who has the same respect toward persons in all things, wills that all men be saved and come to a knowledge of the truth. It is also the eternal counsel of the most high God, to bless, to justify and to sanctify men, by remitting sins in Jesus Christ the only begotten Son and sole mediator, by mere grace, on account of his Son alone, who has made man, suffered and died to expiate the sin of the whole world; through faith in Jesus' name, not by merit or by works which man himself has done. On the other hand, however, [it is his counsel] to damn the unbelieving because of their own sin and guilt, because they have not received the savior exhibited to them.24In this passage, Bullinger again referred to God's desire that all men might be saved and come to a knowledge of the truth. Rather than speaking of God's decree of salvation and damnation, he spoke of God's "counsel" to bless, to justify and to sanctify men in the one Mediator, Jesus Christ. Furthermore, this gracious "counsel" is "on account of Jesus Christ, who was made man, suffered and died to expiate the sin of the whole world." Those who are damned are damned by virtue of their unbelief, by virtue of their own sin and guilt in rejecting the salvation exhibited to them.
Bullinger wrote:Ibid., 441.
Now believe me, many are offended by your [Calvin's] statements on predestination in your Institutes, and from that Hieronymous has drawn the same conclusion as he did from Zwingli's book on providence. In fact, it is my opinion that the apostles touched upon this sublime matter only briefly, and not unless compelled to do so and even in such circumstances, they were cautious that the pious were not thereby offended, but understood God to desire well for all men, and also to offer salvation in Christ, which itself can be received not by one's own worth but by faith which is truly a gift of God. And indeed the elect are chosen on account of Christ and his grace and not on account of any respect of their own; the reprobate perish truly on account of their own guilt, and not by the malice of God.2727. CO 14:215: "Nam mihi crede plures offendi tuis Institionibus de Praedestinatione editis, ac illud colligere quod collegit ex Zwingli libro de providentia Hieronymus. Mea quidem sententia paucis sublimen hanc causam attigerunt apostoli, nec nisi coacti, eamque sic moderati sunt ne quid inde offenderentur pii, sed omnes intelligerent Deum bene velle omnibus hominibus, ac in Christo offere salutem, quam ipsi, non sua virtute sed fide, vero Dei dono, recipere possint, adeoque propter Christum et gratiam eius et non ullo sui respectu electi sint, reprobi vero sua culpa, non Dei malignitate, perire."
...the concluding portion of Bullinger's letter to [Bartholomew] Traheronus was even more striking with its emphasis upon God's universal promises. Bullinger rejected the position of those who spoke of a small number of the elect: "As a matter of fact, we prefer to insist upon these universal promises and to have a good hope for all."50 This hope was based upon the fact that we were not to inquire curiously into God's secret counsel (arcano Dei consilio), but were to heed the revelation of God's grace through Christ and the apostles. This revelation indicated that God was a "lover of man" (amator hominum) who desired the salvation of all.51 For this reason, the gospel must be preached to every creature.Ibid., 446.
50. CO 14:488: "Quin potuis urgemus universales illas promissiones et omnes iubemus bene sperare."
51. CO 14:489: "Quod videlicet Deus sit amator hominum, quod hominibus bene velit, quod omnes in Christum credentes elegerit ad vitam, adeoque quod omnes homines velit salvos fieri, Unde evanglium praecepit praedicari omni creaturae."
Venema noted that:
It is of course true that this correspondence constituted a small portion of Bullinger's commentary on the doctrine of predestination. But, as noted in our introduction, it does provide a striking and frank account of his position in relation to that of Calvin. Moreover, there are other sources which suggest that this correspondence is representative of Bullinger's position throughout his life.53Ibid., 446–447.
53. Three such sources are: The Decades of Heinrich Bullinger, 5 vols., ed. Thomas Harding (Parker Society, Cambridge University, 1841-52), especially sermon 5 of the fourth Decade: Summa der Christenlicher Religion (Zurych: Christoffel Froschauer, 1558); and the Second Helvetic Confession, an English translation of which is found in The Book of Confessions of the United Presbyterian Church in the U.S.A., chapter 19 (New York, 1970)."
Venema, near his conclusion, wrote:
He [Bullinger in his letter to Traheronus] hastens to add that God takes no pleasure in the death of the wicked and wills that all might be saved and come to a knowledge of the truth--an affirmation made in his correspondence with Calvin in the Bolsec controversy as well.Ibid., 447–448.
And fourth, Bullinger in his correspondence [with Traheronus] emphatically insists upon stressing the universal promises of God and repeats his conviction that it is the teaching of the apostles that God desires the salvation of all.Ibid., 448.
...he [Bullinger] may be described as a "universalist" in the loose sense that he wants to take with utter seriousness those biblical passages which speak of a well-meant offer of the gospel and God's desire that all be saved.Ibid., 448.
While his [Bullinger's] doctrine, therefore, shared the same theological function as that of Calvin, it did so in such a way as to retain an emphasis upon having a good hope for all, upon proclaiming the gospel to every creature, and upon God's desire for the salvation of all. Perhaps the single most important thesis in his articulation of this doctrine [predestination] was that a concern for salvation by grace alone need not require a denial of these emphases.Ibid., 448–449.