Another idea for bringing the subject up at first is to just ask them what their policy and approach is to working with self-injury. You don't actually have to tell them at that point that you do it. See if their answer is something that you can deal with. If they work for an agency, they might be more bound by agency policy and required to take action that they might not personally feel is warranted.

Apparently, policies will vary. I have never had a therapist suggest hospitalizing me for SI, and I have shown them wounds that were just hours old (small ones), and I've written saying that I really wanted to cut and didn't care whether I did that night or not. Once I was saw T and had a wound that was still bleeding (not in a visable area) that I didn't mention, but I bet he suspected something from my facial expressions.