Look, no one's calling you a bigot, but if your first thought when hearing that someone has a mental illness is 'watch out', that's a bias. It's not right or wrong, it just is. =/
I also acknowledge that the presence of mental illness can correlate with violence, in the cases of people who are borderline, psycopathic, suffering from PTSD, etc. But there are plenty of mental illnesses like depression and anxiety that rarely hurt anyone but the sufferer, and they're actually far more common.
That's why the stigma of 'mentally ill = dangerous' causes a lot of problems: people who wouldn't hurt a fly (AND people who might hurt someone in the future) often choose not to seek help because they don't want the label.