Before broadcast media and when only nobility and spiritual leaders could read, with the earliest record where the term was used being 1535.
Salesmen or musicians arriving in a new village or town would announce their presence by ringing a bell or beating a drum. The reason for this was to gain the attention of those living in the village or town.
Once a crowd had gathered around the salesman or musician, the stranger would go about his business selling merchandise or performing in exchange for a meal and a place to sleep the night.
Originally, the term was to “drum up trade” however, in the past century, the term has become to “drum up business.”