Well, that depends, how far are you willing to drive?
Within the area, there are lots of options. The best big-name trainers probably within reasonable distance would be Mette Rosencranz in Topanga Canyon (April Atwell is at Topline, also in Topanga Canyon), or Kristina Harrison in Los Feliz. Hilda Gurney is up in Moorpark, as is Jan Ebeling (I think), though that’s probably a bit of a hike (though would likely have pretty decent turnout).
Not so big-name trainers that are good and close to BH would be LAEC’s lot: Lehua Custer, Jaye Cherry, LJ Banks (poor turnout, but you get great trails and access to covered arena when it rains). Pat Lincourt (at the Paddock in Los Feliz, so, again, poor turnout), while primarily a jumper trainer, is also very serious about dressage, is an L judge, is competing her own dressage horse at 4th level (I’m pretty sure) has a solid background with Iberians, and has always impressed me with her integrity and putting the horse first (I’m sure lots do, but with her it was always clear and upfront that that was the case). Pat may also still travel to train, if you end up somewhere else. Middle Ranch (Lake View Terrace area) has a few options, also. Lars Holmberg and Ulf Wadeborn come to mind as being well loved by their clientele. I’ve also heard good things about Susan Regalmuto, who also has experience with Iberians (also at Middle Ranch). Dane Lawrence (also in Lake View Terrace) has a lot of Iberian experience (from what I’ve heard).
Straight up the 405 is Carin Bannos at her own facility (CB Sporthorses). A smaller facility, and she is a fantastic trainer all the way up the levels. All horses get turnout every day (some turnouts are small, but some are large-ish round pen size). Her primary experience is with warmbloods & friesians, but has certainly worked with her fair share of Iberians.
Maggie Broekman is also a fantastic trainer (I think she’s itinerant mostly now, as she travels a lot). Her eye and feel is as good as it gets. Left my horse in training with her for a few weeks when I went overseas - when I got back, I was pretty amazed. I didn’t even know he was capable of such talent!