Patimokkha Rule On Bathing I recall having read somewhere that monks are allowed to bathe only once every 15 days. What is the actual Patimokkha rule behind this ? Also, what is the reason behind this rule and what are its possible benefits ? Is there any specific story corresponding to this rule ?
It's Pācittiya 57:


  
  Should any bhikkhu bathe at intervals of less than half a month, except at the proper 
  occasions, it is to be confessed. Here the proper occasions are these: the last month and a 
  half of the hot season, the first month of the rains, these two and a half months being a 
  time of heat, a time of fever; (also) a time of illness; a time of work; a time of going on a 
  journey; a time of wind or rain. These are the proper occasions here.
  
  
  (Thanissaro, trans)


The reason is ostensibly that bathing is an unnecessary luxury. The benefit to the rule is that monks will not become overly attached to cleanliness and that they will not become a burden on society. The story behind it is that the king was unable to bathe because the monks were bathing. 

Note that the rule only applies to bathing; showering is not mentioned.