After you purchased bibisco you received an email like this (if you can't find it check the spam folder):
Press the button View Product; the button takes you to a page where you can download the new version of the application:
If your operating system is Windows or Linux, after download:
unzip downloaded file
if your operating system is windows launch bibisco.exe; if your operating system is linux launch bibisco
If your operating system is Mac:
open downloaded dmg file
follow the instructions
Problems? Take a look: