My Sig232, which is similar in size and function to the Bersa 380, is downright unpleasant. After running a few magazines through it I have to go dry-fire for a while to stop flinching. I used to have a Colt Govt. 380, which is also small but uses a locked breech instead of blowback. That one was fine by me, but my wife hated it. I haven't bothered letting her try the Sig.
Recoil is caused by bullet weight, muzzle velocity, and muzzle blast. It is counteracted by the weight of the gun. 380 ammo is smaller than 9mm, but the gun is smaller yet. Blowback actions also transmit more of the initial recoil to the hand than short-recoil locked-breech systems do.
I'm not an expert pistol trainer, so take my opinion for what it's worth (i.e., not much); Trying the 6906 might be a good place to start, but if she likes the little Bersa, try to find something single-stack that fits her hand well. I guess you could also have her try the 6906 in single-action mode, so she doesn't have to deal with the long DA trigger reach. That might be a good compromise, and wouldn't cost any extra just to give it a try.