Can't help with the beach/bungum worms, as I'm terrible at catching them. But there are two other types of worms that are easily collected, seaweed worms and a type of lug worm.
Seaweed worms are small worms that look a like garden worms. They can be found in the beds of seaweed washed up on the shore. You are looking for areas where the seaweed beds build up over time, not just what washes up after a big blow. You dig down to where the weed bed meets the sand underneath and will find the worms in the bottom layers of the seaweed. Don't be fooled by their small size, they are a gun bait,