Check out the thread here on this forum "ammuntion choices for those carrying .380s".....there is a wealth of info there.
Also, remember that "reliablity" is a bit subjective and can vary from handgun to handgun.
You might try the Federal Classic HP; it has reasonable ballistics, feeds well in most good quality 380's, and is spoken highly of by Steve Camp in one of his books, which is good enough for me. Just make sure it feeds in your particular Bersa example.
Others report good results with the hot Cor Bon load or the heavy-for-caliber Remington Golden Sabre.
Hello. Though I've read a few reports to the contrary, the Bersa .380 I own and a few others that I've shot have run quite smoothly and reliably (as in 100%) with any JHP I've tried. Due to its aluminum frame the bottom of the feedway is the frame ala 1911 and really flat nosed or sharp edged JHP's could begin to ding up that area I believe. For that reason primarily, I usually suggest the Federal 90-gr. JHP. It's rounded ogive shouldn't create any problems. With some magazines, any JHP will work fine as it will be held high enough that the offending portion of the bullet profile won't contact the lower portion of the two-piece feed ramp.