How long I can see bot activity log?

As long as you're running vBSEO, and have that option turned on in vBSEO, you will see the stats as soon as a bot visits a page on your site.

Go to the vBSEO Control Panel (vbseocp.php) and turn on this option:

Log & Tracking Options
Log Spider Activity in your Forums?
Set this option to 'Yes' to log Search Engine Spider activity on your Forums. This option requires the vBSEO Google / Yahoo Sitemap Generator installed.

Note: Access your Spider Activity logs via your sitemap reports interface ( http://www.fireblades.org/forums/vbseo_sitemap/ )