You already have some good suggestions. Consider them all and see what might help give you the results you want.
I'll add to DHMom's list .......
4) If you have one of the newer machines with the wider 9mm feed dogs, your fabric may not be getting fed into the machine straight because the foot being used is not fully covering the feed dogs. Ask your dealer about the foot required. For the newer Berninas it would be the 97D
5) Do you have the single hole plate in? If you have the zigzag foot, the fabric has more slippage possible, especially if you have the 9mm feed dogs.