based on that one rumor/anecdote about them
If I remember correctly, the story about William, Bentinck and the innkeeper's daughter was shared around by none other than Keppel's father-in-law, which, considering William III was close with Keppel and the latter's family might suggest that this was a titbit William himself may have shared as a joke or anecdote from his younger years.
However guarded his public persona, he appears to have been a very warm, personable character when among people he considered his friends, so there might be a grain of truth to this story, which, given it is hearsay recorded by a third party at best, should still be taken with a pinch of salt.
That said, Hans-Willem Bentinck and William III were close friends ever since Bentinck had started out in William's service as a page in their middling teens, and William, too, was involved in Bentinck's romantic life.
William tried his best to convince his cousin Charlotte Philliberthe van Nassau-Beverweerd, whom Bentinck had fallen one-sidedly in love with, to marry his best friend, but it appears that "Lott", as William called her, was not interested in Bentinck's attention. She never replied to any of William's letters on the subject despite promising to give an answer, and Bentinck, presumably heartbroken at the rejection, met and married his first wife Anne Villiers, coincidentally a lady in the retinue of William's own new wife Mary, a few years later.
Here, again, William stepped in to help his best friend's romantic life along: because the Villiers family could not raise a suitable dowry, which prevented their daughters from marrying and thus necessitated their 'working' for their own upkeep in court positions, William stepped in and settled a dowry on Anne so that she and Bentinck could get married with some financial security and according to their social status as nobles.
It's quite interesting to think that William, who for himself considered marriage as a matter of state as per the nature of his position, saw the value in and appeal of marrying for love, and did what was in his power to see his friend happy, and in love.
Perhaps Bentinck's romantic streak, displayed in several luckily preserved letters to Anne, rubbed off on William to some degree as well, seeing as, given time, he and his wife Mary, too, developed a close and very loving relationship.
