A simple question that could hide a multitude of issues.
You need to give you operating system and a full description of the problem you are trying to solve with any error messages in full.
Simple answer:
You need to be an administrator. Type services in the search box and click on services in the program section.
Find the bonjour service,right click and select start.
I am afraid that is not true, uninstalling iTunes does not uninstall Bonjour. If you want to uninstall Bonjour you have specifically uninstall it.
http://support.apple.com/kb/HT1923
Yea, that was my bad. When I think of uninstalling iTunes, I usually uninstall everything that came with it (Apple Application Support, Bonjour, Apple Software Update, Apple Mobile Device Support, Quicktime, and iTunes).