Using a string function (eg:  LEFT() , MID())  to break up the long label string into short sub-strings can be accomplished by creating calculation fields and then displaying sub-strings one by one vertically on the bar chart.  Follow along with a sample packaged workbook found in the Attachments section of this article.

Information about string functions is available in Tableau Online Help.

Example:
1. Create calculation field [Substring1]
LEFT([Text Label],15)

2. Create calculation field [Substring2]
MID([Text Label],FIND([Text Label],",")+1,14)

3. Place [Substring1] and [Substring2] on [Text] mark label.