While most scholars are reluctant to comment on the debate, I would argue with Michael Young that James I did have sexual relationships with men. The idea of homosexuality/bisexuality did not exist in the seventeenth century, so the term does not really fit what he was doing. The sources on this would be:

Young, King James and the History of Homosexuality, (which just came out with a new edition)

Bergeron, King James and Letters of Homoerotic Desire (this is more of a literary study and is weaker than Young's, but it has the relevant primary texts as an appendix)

Akrigg, The Letters of James VI and I (The standard printed edition of James' letters)

Lockyer, Buckingham: The Life and Political Career of George Villiers is still the standard biography of Buckingham, but does not comment on his sexual relationship with James.

Overall it's impossible to prove whether James really had sex with Esme Stuart or George Villiers, Duke of Buckingham. However, his relationships with them was close enough to resemble intimate relationships between men and women. The most recent work that covers in depth the relationship between James and Buckingham refers to a "supposed" homosexual relationship (Cogswell & Bellany, Murder of King James I, p. 525).