Bunyan, a Baptist, adopted the Calvinist theological doctrines which believed in man's total depravity and unconditional election. According to the Westminster Confession of Faith, 1647: Chapter VI Of the Fall of Man, of Sin, and of the Punishment Thereof:
I. Our first parents, being seduced by the subtilty and temptation of Satan, sinned in eating the forbidden fruit. This their sin God was pleased, according to His wise and holy counsel, to permit, having purposed to order it to His own glory.
I don't think that the authors mean that sin or the fall of man pleased God (gave him pleasure in any spiritual sense). The Baptists and Calvinists, quite to the contrary, believe that sin angers God, that we are "Sinners in the Hands of an Angry God," and that God's ways are quite unknowable by man. What the authors of the this document mean, and what Bunyan likely believed himself, is that God permitted the fall of man to happen, that it was foreordained as inevitable. Since God is omniscient and omnipotent, He obviously saw this coming, and so it was part of His plan to bring mankind into reconciliation and salvation.
According to the Calvinist Westminster Confession of Faith (1647), "Man, by his fall into a state of sin, hath wholly lost all ability of will to any spiritual good accompanying salvation; so as natural man being altogether averse from that good, and dead in sin, is not able, by his own strength, to convert himself, or to prepare himself thereunto" (Ch.10, Sec. 3). Believing that man is born into Adam's original sin is nothing new in Christian theology, but the Calvinists take it to the extreme, saying that man is born dead and condemned to hell, and it is through no will of his own--only through Divine Intervention--that he is able to attain salvation. One can only assume that Bunyan believed that his recurring nightmares were Divine signs, even voices, plaguing him to repent and become reborn.
The Calvinists believe that the sinner is likewise unable to regenerate himself, regeneration being a "change by which holy affectations and purposes are substituted for the opposite motives in the heart" (Webster's online). Calvinist Theologian R.L. Dabney says:
No sinner ever makes himself to choose God and holiness, because every principle of his soul goes infallibly to decide the opposite preference. Therefore, whenever a sinner is truly regenerated, it must be God that has done it. Take notice, after God has done it, this new-born sinner will, in his subsequent course of repentance and conversion, freely put forth many choices for God and holiness; but it is impossible that this sinner can have put forth the first choice to reverse his own natural principles of choice.
To further complicate regeneration, the Calvinists believe in God's election, or predestination. According to the Confession, "Some men are predestined unto everlasting life and others foreordained to everlasting death...These men [are] unchangeably designed; and their number is so certain and definite that it cannot be either increased to diminished" (Ch. 3). Bunyan later preached at length regarding conversion, regeneration, and predestination, and he even went so far as to make a "Map Shewing the Order and Causes of Salvation & Damnation" (see Appendix) in which "the line of grace" extends to the "Election, Upon Which Standeth" directly from the "Son" (Jesus), who resides with God, Father, and Spirit in heaven. Another "Line of Justice" extends from the "Son" to "Reprobation Upon Which"..."Standeth the Convenant of Works," which, after a series of levels (like Dante's Inferno), leads to the "Hell You Bend, In the End."