The drop down menu is nothing to do with the Recycle bin, that is part of the Windows Explorer "recently used directories."
It has nothing to do with what files you had, at one time, in your Recycle bin.
You are chasing rainbows.
If you have the Pro version of Vista, then you can run the Group policy Editor to set your clearing out of some of the "recent tracks" and history of places you've been when you exit Windows. You could also search for some tools that will perform that clear out of your tracks when you exit Windows.
But you really are not going to gain anything in the recapturing of space with any of that.
I am using Windows Vista with Mozilla Firefox and frequently clean out my recycle bin after deleting files. Although no files show in the recycle bin afterwards, drive and file names show up when clicking on the drop down arrow. I How do I get rid of this information? I would either like to get rid of the drop down arrow or make it so that nothing shows when I click on the dropdown arrow. Thanks.