As of version 1.2.1, you can append
&P[ixPlugin]
_ixFilter=[ixFilter]
to the URL, where ixPlugin is the plugin id (you can get it from the URL that it takes you to when you export a filter), and ixFilter ix is the filter id (you can get this from the URL of a filter). For example:
http://my.fogbugz.com/default.asp?pg=pgPluginBinary&ixPlugin=1&P1_ixFilter=4
You can also append a search string in version <1.2.1:
&P[ixPlugin]
_sSearch=[search]
For example
http://my.fogbugz.com/default.asp?pg=pgPluginBinary&ixPlugin=1&P1_sSearch=assignedto%3a%22me%22