Very credible. We have primary sources from contemporaries detailing James' affection for men, in particular the Duke of Buckingham, George Villiers, also known as 'Steenie', and we also have letters surviving from James himself that were written to Villiers.

It seems as though James had a couple of court favourites, the other being Robert Carr, though the Oxford Dictionary of National Biography is a little cautious about pinning down the exact nature of their relationship. Quote: "The exact nature of his personal relationship with James remains difficult to assess. Carr enjoyed constant and unique access to the king's person, day and night, at Whitehall and at the hunt. The king, it was reported, would pinch Carr's cheek in public, smooth his clothes, and gaze at him adoringly, even while talking to others. Although historians disagree about whether the relationship was sexual the intensity of the king's love is evident in at least one of his few surviving letters to Carr." ODNB link (login required).

For contemporary sources, John Oglander (knighted by James) wrote "[James] loved young men, his favourites, better than women, loving them beyond the love of men to women. I never yet saw any husband make so much or so great dalliance over his beautiful spouse as I have seen King James make over his favourites, especially the Duke of Buckingham." Another source from one Bishop Geoffrey Goodman also comments on how little James 'converses' (i.e.; sleeps with) his wife Anne, and there is a reasonable amount of moral judgement from other contemporaries on James' actions. Fischlin and Fortier (Royal Subjects, Essays on the Writings of James VI and V, 2002, p. 349) suggest there was an 'unholy trio determined to castigate James and his court on moral grounds whilst offering titillating examples'. Fischlin and Fortier also go on to suggest that later Victorian writers who wrote about James built on this judgement, particularly when the letters between James and his favourites were first originally published.

A Google Book of the letters can be found here and are incredibly affectionate. In December 1623 James writes to Villiers "[....] and that we may make at this Christmas a new marriage ever to be kept hereafter: for, God so love me, as I desire only to live in this world for your sake, and that I had rather lived banished in any part of the earth with you than live a sorrowful widow's life without you. And so God bless you, my dear sweet child and wife, and grant that you may ever be a comfort to your dear dad and husband."

I think if you're looking for the usual understand of 'prefer the company of young men [plural]', as in had acres of lovers, you might be a little disappointed. I would argue that James was at the very least bisexual (I'm not certain on the closeness of his full relationship with Anne), but had his particular favourite courtiers that he would have very intense relationships with; Carr being one and Villiers being another. He's certainly a very interesting monarch to look in to when you get digging through his letters and sources from the time.