Tie or bungee the bag to the pad. Most sleeping bags have at least one tie down set at the foot (even my $20 off brand). Run some paracord, rope, string, or a bungee from one of the tie downs under the mattress and to the other tie down. If your bag doesn't have any tie downs (more common on rectangular bags), you can see about sacrificing the last inch or so of space at the foot of the bag for a tie down.
I first tried this with my summer weight bag/liner, which is just a thin fleece inner layer with a nylon outer. I toss and turn a ton at night and usually wind up with the bag upside down and off the pad while being twisted in the middle; awkward, considering it's a mummy bag. Just using the foot tiedown was enough to keep the bag put on my Big Agnes mattress. There was a smidgen of shifting at the top end, but it was surprised me how little the bag actually moved with only the foot tied down. It was at least enough to keep me on the mattress and the bag from constricting like a boa.
I haven't tried this with rectangular bags, but traditionally mummy bags have always moved a lot more than rectangular bags in my personal experience.