Hypnosis is a broad term. What you're mostly interested in is hypnotherapy. Reading some books is useful, but it's similar to reading a book on psychotherapy. You need practice.
The books you cite are good --
Elman has some good basics. Spiegel & Spiegel (Trance and Treatment) is very good (written by 2 psychiatrists). Erickson isn't going to be summed up in a book. Everyone has a different take on what he did (check out books by Jay Haley, Sidney Rosen, Bandler and Grinder, and by Erickson himself). Then watch videos.
The ASCH courses are useful for the basics and they usually involve small group practice, which is where the money is. I've been doing hypnosis work since I was 20 years old, starting as a layman and then learning it professionally. ASCH hours also qualifies you for the American Board of Medical Hypnosis (really more like a certficate than a real board certification, if that makes sense).
My best suggestion is to use it in at least small pieces with all your patients. Try it out. It's not just about induction. Inducing someone is the easy part. There's many levels beyond that that really gets at the meat of the trait vs. state debate, the idea of communicating with the unconscious without trance, and the nature of psychotherapy in its various forms. And most importantly, get a good supervisor (and like any therapy supervisor recognize they will likely come from a school of hypnosis/hypnotherapy training, so get another supervisor later).
As for the title of the thread, applying hypnosis to depression and anxiety, anxiety is easy because the nature of trance involves relaxation (relaxation, concentration, dissociation). Teaching self-hypnosis is then a useful strategy as well. Depression varies. Some approaches can involve visualization exercises, use of suggestion, metaphor to guide through the struggle they're going through, or use of regression and their heightened state of concentration to do work that might take longer in a normal waking state. Imaginal exposure for example could be used as well in a systematic desensitization. Lot of options, for those interested.
As others have said, go with the reputable sources -- ASCH (has local branches around the country), SCEH. There's also Erickson Institutes and a foundation with trainings.
As for your psychologist supervisor, my experience is that like in all of medicine, people carry the biases they were passed on from their teachers, usually without exploring it much on their own. I doubt that supervisor has much experience using it, or has reviewed much of the literature on it.