GoVol98,
Start at 10 yards with a proper benchrest and manually cock it so you're firing single-action. Take your time. The groups will tighten and once they do continue at 10 yards with proper benchrest, but begin to shot it double-action first shot, single-action second shot.
The drill I used was DA, SA, decock. DA, SA, decock. DA, SA, decock...
Once you get the groups you want from the bench you'll have confidence in the Beretta. Then stay at the same 10-yard distance, but shoot from your normal standing position. Repeat the same drill as above.
Once you get the groups you want at 10 yards, start moving the target back five yards at a time. It took me forever to get used to the DA/SA on my 92FS, but it can be done for your 96.
You have an excellent firearm. My Glock 23, which is a 40 S&W, I am more accurate with 155g loads than 180g loads. Notice I said I was more accurate, I am sure the Glock could care...
The important thing to remember is have fun and enjoy your new Beretta; try not to get overly frustrated. Ask yourself how long did it take where you were a good shot with your .38 snubbie. Now you are learning a whole new handgun with different handling characterisitcs, sight radius, trigger action, etc.