Did John Bunyan believe that irresistible grace was only for the elect?
In short the answer is no. Irresistible grace is the belief that only the people that God has chosen can receive saving grace. This theology was first introduced to us by John Calvin. Calvin believed that God had predestined certain people to be saved and to go to heaven. He taught that these pre-chosen people were the only ones able to acquire the saving grace that God has offered to all of his people.
John Bunyan was born in 1628 in Estow, Bedfordshire. He is most well known for writing The Pilgrim's Progress. Some people who have read the book, claim to see predestination themes in the book, but this has never been addressed. John Bunyan was a Puritan. When he was a young man, he played games and did things on the Sabbath, which was greatly preached against. He heard a sermon on this, and it changed his life. In the 16th, 17th and 18th century people were starting to take a stand for religious purity in Europe. Puritans believed that Church of England was not pure enough and they were still associated with the Church of Rome. Puritans wanted to make changes of purity within the church, instead of separating from the church.
John Bunyan believed in the theology that all of God's people were eligible to receive the grace of God. He was not a Calvinist and did not believe in predestination. He thought all of us are allowed to receive this grace, if we just choose to follow Christ and live our lives accordingly.
It may look like at first glance that John Bunyan as a puritan would adhere to the so-called Calvinistic thought about predestination and salvation. However, only by noting the insistence he presents on personal ethic in his famous prison book Pilgrim's Progress, we tend to start thinking toward his catholic side of the coin faces. He seemed mostly concerned in this book to show the need for growth in the Christian character through the suffering in seeking perfection reaching the cross and the crucifixion point at which one is saved. But at the end, he may have proved that no matter how much one puts of himself unto his own salvation search, it will be what Christ has done that will alleviate his burden for good. He may have proved the pilgrim made no progress until he noticed how useless his effort was for the purpose of personal relief in salvation except by Christ's work. If we stick to the analysis of this single book, we may conclude, then, he was a puritan with a sense of personal responsibility as acute as any catholic but not apt to count his effort on a pair with Christ's, and too involved in his salvation pursuit to be counted among the traditional viewers of Calvinistic theology who rely on the allegation of predestined salvation annointing.