First of all, the book published in 2016 from Yale English Monarchs by Bates is hardly deserved to be categorized as 'old'. So, I afraid that you mixed his newer and much lengthy biography on William the Conqueror with the older, but much shorter (and readable) one.

Bate's old biography from Tempus is short and still regarded as well-written, I suppose, but the publishing year of the 1st edition (1989/ illustrated ed. 2001) is out of question in your criteria.

Then, if one of the Penguin monarchs series by Mark Morris (2016) is obviously too short for you (I hope), Mark Hagger's William: King and Conqueror (2012; 256 pp.) is almost only remaining choice for you, I suppose.

He is an excellent scholar on the early history of Normandy, as I mentioned in I'm curious about every day life in Viking Normandy around 950-1050 AD, but this biography is reviewed by some leading scholar of elder generations by George Garnett as not without flaw (neither very comprehensive nor very compact). You can also read another review of Hagger's book by Mark Marris here for open-access.