A guy I know uses a "Husky" brand red and black square tool bag which has wheels and a retractable handle. Two bowling ball boxes fit perfectly inside with lots of room for shoes and towels on top of the boxes. The bag has lots of exterior compartments which allows him to see the items he may need vs. digging around in large zippered compartments searching for an item.
He also carries a single joey bags on top for a total of three balls.
The bag is very solid and rolls beautifully and the retractable handle is super strong. He bought it at Home Depot. He tried a similar bag from Lowe's, but it was not of high quality. He says he likes it better than any two ball bag he has ever owned.