Hej Johnny,
Det er lidt tricky, men det kan lade sig gøre

function GetBmpDPI(Bitmap: TBitmap): LongInt;
var
Stream: TMemoryStream;
Data: Word;
A: Double;
begin
try
Result := 0;
Stream := TMemoryStream.Create;
Bitmap.SaveToStream(Stream);
Stream.Position := 38;
if Stream.Read(Data,2) = 2 then
begin
A := Data;
Result := Round(A / 39.370079);
end;
finally
Stream.Free;
end;
end;