Is there a pistol out there in 9mm that is roughly the same size as a Bersa 380 and roughly the same cost?
Kahr.
Have you looked at the rest of the Bersa line? They have some pretty small 9mms available.
Meeting your criteria of size and price is the Kel Tec P11. May even be a little thinner in the grips than the Bersa. Never a problem with mine. Sells for about $250 around here.