This long-requested feature was added in the summer of 2014, for AIR 2.3.1.
Here's how to search within any bin you have created, or any bin created by another user which you have permission to view.
Select a bin from AIR's bin drawer, viewing it in its open state:
Click the "search/map" button. This will open a search page in AIR with the bin ID already filled out in the search field. Simply use filters and/or add additional terms to the search field, as you would any other search, and the search will be performed within that bin.
Note: When using the search field while searching within a bin, remember to make sure that the bin ID is outside any parenthesis you create around additional search terms, so AIR interprets the search as a "bin X AND Y terms instead of "bin X OR Y terms."