I have brought up being suicidal with my therapist. She was visibly uncomfortable every time this topic came up - I can't blame her, she had little to no experience in psychotherapy but that's another story - but we still talked about it. The usual questions from her were 'do you have a plan?' (My answer was always 'I know my options'), 'do you know when you are going to do it?' (A honest answer of 'no'), 'what's keeping you here?' (My family will be sad), and then she always suggested contacting the crisis team and going to the hospital (once). I refused crisis team every time. When I eventually find another therapist, I will make sure to be as non-specific as possible regarding my choice of methods/plans etc. This was NHS therapy in the UK.