I think, based on your question, that you want to see if Bar in a given class instance is equal to test.
If so, you can leverage the ToString() override:
Public Class Foo
    Public Bar As String = "test"
    Public Overrides Function ToString() As String
        Return Bar
    End Function
End Class
and your case statement then becomes:
    Dim foo As New Foo()
    Select Case "test"
        Case foo.ToString
            ' It worked!
    End Select
You could also implement a default property, but that isn't as clean because a default property are required to have a parameter.
Public Class Foo
    Public Bar As String = "test"
    Default Public ReadOnly Property DefaultProp(JustUseZero As Integer) As String
        Get
            Return Bar
        End Get
    End Property
End Class
which would then be called as:
    Dim foo As New Foo()
    Select Case "test"
        Case foo(0)
            ' It worked!
    End Select