Yes, Bitmap is a managed class. But it is a very thin wrapper around code in gdiplus.dll, the unmanaged code that implements GDI+. Bitmap data is allocated in unmanaged memory. To ensure this memory gets released as soon as possible, the Bitmap's base class (Image) has a Dispose() method. And a finalizer to ensure that memory is released when the client code doesn't call Dispose(). Calling Dispose() for bitmaps is pretty important because the Bitmap class is so small. You can create a *lot* of Bitmaps before the garbage collector kicks in, running the risk you'll run out of available unmanaged memory.
If you have a Bitmap member in your class, you should indeed also provide a Dispose() method. You'd simply call the member's Dispose() method, as you do. You do NOT need a finalizer since your own class does not have any unmanaged resources that need to be released. The finalizer of the Bitmap member is sufficient. Since you don't have a finalizer, you don't have to worry about GC.SuppressFinalize().
I don't understand why you'd call CloseMap/Dispose() in the constructor. If the bitmap is just a temporary variable instead of a class member, you'd just call Dispose() on it when you're done using it.