By BPD do you mean Borderline Personality Disorder or Bipolar Disorder? People often use BPD for both.
With regards XXXXX XXXXX cycling mood you have noticed, has Bipolar mood instability been considered/ruled out?
It's actually quite common for people who suffer from BPD to have great difficulty trusting a therapist and forming a good therapeutic relationship. As the most effective treatments for BPD, and PTSD are both psychotherapeutic (not medication) finding a therapist that you can work with should be the main focus. A skilled Dialectical Behavior Therapist (DBT - the therapy that is specially designed for BPD) should be able to help you settle into therapy. DBT therapists have deal work with this problem all the time....it's their job and their responsibility to make it work for you.
Would you consider trying to locate a good DBT therapist?
If you do wish to locate a DBT therapist then I suggest you contact the American Psychology Association (APA) for assistance with locating a Psychologist trained in DBT; take a look at the APA locator service here. You can use this to find Psychologists in your area and there is a phone number you can contact if you want a referral arranged for you. Also, take a look at an article published by the APA here. It's an interview with a senior Psychologist and covers some of the things you should consider when you looking for a Psychologist. I hope this has been of some help, best of luck!