1). You are not a bad Mom- it sounds as though you are being really hard on yourself.
2). Just the fact that you can recognize that your son has behaviors that need to be examined by a therapist shows that you care and want the best for your son.
3). Learning how to parent effectively with BP is a huge challenge. My daughter is four- and when she pushes my buttons to the point where I fear that I'm going to explode- I just say, "Mommy's having a mood right now- both of us need to calm down." Then if we're in the house- I'll walk to where she can still see me and pace back and forth- I just remind myself not to rush and make a decision and I try to see things from her perspective. Seeing a therapist who can help you learn some coping strategies (all kids will test parents limits) would help you get more confidence and feel better about your parenting approach.
4). Regarding the tantrums- have predictable consequences. My daughter knows that she gets one warning for a time out, then I count to five if she needs to do something (e.g., pick up after herself), then after that she screeches like a holler monkey. But she at least knows what to expect when she chooses to behave poorly.
5). I have a lot in common with you- I grew up with a mentally ill mother who required hospitalization. I was lucky to have an extended family who was able to help me. Due to my illness- I went three months last year without being the primary caregiver of my daughter. You just have to accept that illness can happen to anybody. It's how we respond & move forward with what matters.

Keep posting on here- we're here to support you.