As no-one has replied yet, Baz, let me have a guess. Beggars and street buskers usually have a receptacle of some kind into which they hope kindly passers-by will drop some money. In earlier times, when men invariably wore hats, a cap would be passed round to collect tips for bus-drivers and so on. It strikes me that such receptacles/caps are pretty much a form of 'bag', so I wonder whether that is the source of your saying, which I must confess I have never heard used.
The idea behind it, therefore, is one of receiving "money for nothing very much" as it were, which seems to be what your drivers are doing.