Hi there!
After worming for 20+ years around Jervis Bay the easiest and most effective method I've found for keeping worms is simply a bucket of seawater with an aerator. I use a 20ltr bucket and only about half full and replace the water every day.
Doing this will keep them alive for 3-4 days.
Try using your fingers to catch them if you can, and go for some smaller ones to start. They are easier to pull out, are less damaged because you don't need to squeeze them so hard and therefore keep alive for longer.
We have some monster greenhead worms on our local beach but I usually leave these for that reason unless we are heading outside to fish.
They are THE best bait to use in an estuary, the beach or bottom bashing in 60mtrs of water. Caught many nice reds on large beachworms.
I hope this is helpful and good luck with catching some.
Cheers