There is a good article on how to control URLs with buckets:
https://adeneys.wordpress.com/2013/07/19/item-buckets-and-urls/
And also existing question from StackOverflow:
How do I bucket Sitecore items on something other than their creation date?
This will help you to arrange your buckets in the more appropriate way. However, in case you want to keep the structure of your buckets as date folders, but only adjust the dialog, I afraid this would not be an easy to do, unless you upgrade to at least Sitecore 7 where you get search interface.
Buckets were became integral part of Sitecore 7 to work along with new search features, so having new interface that performs search against indexed items from your buckets does the job. Unfortunately it was not yet in 6.6
Of course, if you are desperate to have this search dialog simplified for business users without removing buckets or changing physical storage pattern, you may consider more complex way to sort this problem (this is just a theoretical approach how I would do in this case, each step may require much R&D labour):
- Using reflection, open find and open the dll responsible for that dialog (is it Sitecore.Kernel?) and find exact class responsible for that particular dialog
- Copy code of original class / or inherit from it
- Override the component that displays tree and make it show flat list of documents
- Re-reference dialog to use your component instead of original