The Bersa .22 needs high velocity ammo to cycle it properly. There are exceptions to this. Some report it operating fine on bulk ammo after theirs was well broken in (500-1000) rounds, but not everyone. My wife's would only shoot Remington Golden Bullet in the 225 bulk box. We tried 6-7 different brands, including CCI Mini Mags & no go.
Then I started checking the bullet when the other brands when they didn't chamber & when they did, then also checked the Remington when did chamber & found what seemed to be the problem. The Remington bullet seems to be loose in the case. You can turn it & it also flexes almost to the extent that you'd think they would fall out, yet they don't. When I checked rounds that had chambered, I found tiny nicks in them, but in different spots on the lead. The bullet in other brands are rigid & unmoving in the case. When I checked these when they did not chamber, or the few times they did chamber, There was a gouge partially around the bullet, always at it's base.
This told me the bullet was hitting a sharp edge on the way into the chamber. Since the gouge on the other brands was always in the same spot & extended around the base of the bullet, it led me to think it was the sharp edge of the chamber opening. The bullet in the Remington, being able to flex, allowed it to be chambered & the little nicks in the bullet appeared in different positions.
I took a cone shaped dremel bit & spinning it BY HAND, just barely put a chamfer in the opening into the chamber. Since then, she has been able to add several more brands to her arsenal of ammo that cycle okay. Still not perfect, but much better. Others have reported similar problem with the sharp edge on the little ledge just prior to entering the chamber. If this is your issue, it will appear as a tiny nick in the bullet, not a long one around the lead.
Another common cause has already been mentioned, the magazine. As you load the magazine, carefully watch the upward slant of the top round. If it starts flattening out, the mag is the problem. With all 10 rounds loaded, the mag inserted in the pistol & the slide locked back, the top round should have an upward slant & be pointed at the chamber.