Basically the way you are opening the two files ends up making TextMate think that your "project" is Bar which is why they are both showing Bar as the "project" folder (which is what the Bar in the screenshots actually is).
Using the following ends up with t as the "project"
$ mkdir t
$ cd t
$ mkdir foo bar
$ echo foo > foo/baz.txt
$ echo bar > bar/baz.txt
$ echo t > ./baz.txt
$ mate **baz.txt
I usually use something like this for my projects:
windowTitle = "PROJECTNAME:$TM_SCM_BRANCH ${TM_FILEPATH/\/Volumes\/VolumeName\/projectfolder\///}"
Which gives me the full path within the project as the projects I work on often contain multiple files with the same name.