I am not an expert on medieval hunting, but since you are asking for sources, here are some good ones taken from the footnote of an article I just happened to be reading (Ryan R. Judkins, “The Game of the Courtly Hunt: Chasing and Breaking Deer in Late Medieval English Literature” Journal of English and Germanic Philology 112 (2013) 70-92). In fact, I am just going to paste the entire footnote here; I hope that is allowed:

Gaston Phébus, author of the 1389 Livre de chasse, stated in an illustrative comment that hunting was one of the three prime aristocratic activities: “Tout mon temps me suis délité par espicial en trois choses, l’une est en armes, l’autre est en amours, et l’autre si est en chasce.” (I have always especially delighted in three things: one is arms, the other is love, and the last is the hunt.) Livre de chasse: édité avec introduction, glossaire, et reproduction des 87 miniatures du manuscrit 616 de la Bibliothèque nationale de Paris, ed. Gunnar Tilander (Karlshamn: Johanssons Boktryckeri, 1971), p. 51, hereafter, Livre de chasse. Women hunted as well as men, but they seem to have been involved in the more social and less physically taxing types of hunting. In particular, women seem to have participated in the bow and stable hunt on a regular basis and to have been very fond of hawking. Though much of his evidence is visual, Richard Almond comes to a similar conclusion in the only book on the subject: Daughters of Artemis: The Huntress in the Middle Ages and Renaissance (Cambridge: D.S. Brewer, 2009), p.150. For more background on medieval hunting, see John Cummins, The Hound and the Hawk: The Art of Medieval Hunting (London: Weidenfield & Nicolson, 1988); Emma Griffin, Blood Sport: Hunting in Britain Since 1066 (New Haven: Yale Univ. Press, 2007); and Robin Oggins, The Kings and Their Hawks: Falconry in Medieval England (New Haven: Yale Univ. Press, 2004). For broad considerations of hunting, see Thomas T. Allsen, The Royal Hunt in Eurasian History (Philadelphia: Univ. of Pennsylvania Press, 2006); and Matt Cartmill, A View To a Death in the Morning: Hunting and Nature Through History (Cambridge, MA.: Harvard Univ. Press, 1993). For a foundational and still-valuable article on the noble hunt as a whole, see Marcelle Thiébaux, “The Mediaeval Chase,” Speculum, 42 (1967), 260–74.

There is also a Middle English translation of the Livre de chasse, called Master of Game made around 1410. I know this is much later than William Rufus, but perhaps one of the books above will cite something older. The only thing I know of that is earlier than Rufus is the short description of hunting in Aelfric’s Colloquy, where the hunter describes several methods (traps, birds, dogs, etc), but those are not royal hunts.