Is it even possible? I mean I searched internet and my phone like for an hour and haven't found such thing as bug report for Microsoft.
Reporting a bug through the phone itself
There is no built in module in the phone that allows you to reports bugs per se. You do have an option of allowing Microsoft (and Nokia if you have a Nokia handset) to gather usage details, etc. automatically.
Reporting a bug on the web
The best way to do this would be through the Microsoft Community Forums. Here, you can either open a new question or discussion pertaining specifically to Windows Phone.
Are you sure it is a bug?
- It could be behavior that has to do with settings that are perhaps not very intuitive. In such cases, you are almost better off posting on Windows Phone SE (this site).
- It could be a missing feature. In such cases, you are better off opening a feature request on the Windows Phone User Voice site.
You can add you suggestions (bug reports) at http://windowsphone.uservoice.com/