This has nothing to do with BS.Player. It is a setting of Windows. What version do you have?
You could check under "configuration" > "Folder-options" and then TAB "Display" (or similar; I translate this from a Dutch WinXP-version; anyhow not "General", nor "Filetypes" ).
Then there will be a checkbox (for me in WinXP it is the 7th from the top) "Hide extensions for known file-types".
Deselect that setting and click [OK].
If it's Vista, I would have to check my laptop. Please let us know.