some explanations about how your code works.

Both formats are very simple, uncompressed files, with almost the same data format; which makes conversion simpler.

I detailed the gd format header in Re: About GD Image Data Output Methods.

I used this for the bmp format details.

Hopefully these comments will explain the rest.

## Get the gd format data as a string
my $gd = $image->gd;

## Unpack the header (we're only interested in the width & height) and
+ strip that header from the image data
my( undef, $width, $height, undef, undef ) = unpack 'nnnCV', substr( $
+gd, 0, 11, '' );

## GD image data is 4 bytes (rgba); BMP image data is 3 bytes; so calu
+late the length the bmp image data with occupy
my $len = length( $gd ) / 4 * 3;

## Pack the required information to create a .bmp header (in two parts
+). (see link above)
my $bmp = pack 'a2 V V V l< l< l< v v V V l< l< V V',

## The .bmp file header has 5 fields (but 2 U16s do nothing so pack 1x
+U32 value 0 for them)
##  sig   file-length (data+header length), 2 unused shorts as U32, an
+d the offset to the rgb data.
    'BM', $len + 54, 0, 54, 

## BITMAPINFOHEADER 40 bytes, image width & height (negative to turn i
+t the right way up!), 
## color planes (1), bits/pel(24), compression type(none:0), length of
+ rgb data, 3 unused fields.
    40, $width, -$height, 1, 24, 0, $len, 0, 0, 0;

## Convert the rgba gd data to rgb bmp data (x skips the alpha bytes)
## And tack it onto the end of the header. 
$bmp .= join'', unpack '(xaaa)*', $gd;
[download]

Of course, the code is crude as .bmps have a multitude of other possibilities, and (as you've seen) I don't even check for truecolor .v. palette in the gd format; but the intention was to give you something that did the job, not duplicate the functionality of image conversion software.

It wouldn't be too hard to handle palette images; but I don't think it is necessary for your purpose.