Search engines are weird. But they turn up some interesting stuff. Like the first race at Hollywood Park July 18, 1986. A horse named "Bukowski" entered with Valenzuela riding. Didn't do well.
I think there may be a picture of Bukowski standing with "Bukowski" and Valenzuela hanging in Bukowski's living room. There are a couple pictures of him with horses and jockeys at the track anyway.
The Bukowski-Society has 2 pictures of Bukowski posing with horse and jockey.
I'm not at home till March 20 to check them and at the moment have only these mini-thumps with me: