I found the solution for your problem. Your declaration should be preceded with this marshaling:
[return:MarshalAs(UnmanagedType.I1)]
so everything should look like this:
[DllImport("Whisper.dll", EntryPoint="Exist", CallingConvention=CallingConvention.Cdecl)]
[return:MarshalAs(UnmanagedType.I1)]
public static extern bool Exist([MarshalAs(UnmanagedType.LPStr)] string name);
I tested it in my very simple example and it worked!
EDIT
Why this happens? C defines bool as 4 bytes int (as some of you have said) and C++ defines it as 1 byte. C# team decided to use 4 byte bool as default during PInvoke because most of the system API function use 4 bytes values as bool. If you want to change this behavior you have to do it with marshaling specifying that you want to use 1 byte value.