Can buldging discs in the lumbar cause pain that wraps around to the abdomen?

No: Pain may go down the legs.

Innervation: Lower thoracic and upper lumbar vertebrae are areas where the nerves that come from those areas can innervate, or supply the sensation to the lower abdominal areas ANS surrounding structures. So bulging discs, that may be pinching nerves could be a cause of pain in the area. You may need other possible causes ruled out though, best wishes.