Does the Bible ever say that God intended for man to be unmarried and worship Him with all our love?

Answer:

Something close to that…Paul was talking about marriage and giving rules for it and then adds that it might be good if others were like him (he was unmarried)… 1 Corinthians 7:32-33  But I would have you without carefulness. He that is unmarried careth for the things that belong to the Lord, how he may please the Lord:  But he that is married careth for the things that are of the world, how he may please his wife.

Again, it is not wrong to be married and in fact it is a blessing of God, but for those who feel called to the Lord’s work and want to remain single that is a good thing also just as Paul did.