Gimp can read and write 32-bit Windows Bitmap files. 32-bit BMP files are read using GDK, but GDK doesn't appear to read the 4th channel, hence ignoring transparency. This bug report is derived from bug 676219 and below I have quoted Jigebren who discovered that the issue lied within gdk-pixbuf:

"In OneLine32(), we can see that the alpha component is simply overwritten with
0xff:
        for (i = 0; i < context->Header.width; i++) {
            *pixels++ = src[2];
            *pixels++ = src[1];
            *pixels++ = src[0];
            *pixels++ = 0xff;

            src += 4;
        }

Not to lose the alpha channel it should be:
            *pixels++ = src[2];
            *pixels++ = src[1];
            *pixels++ = src[0];
            *pixels++ = src[3];

I don't know whether or not GDK is supposed to support alpha in BMP files. But
as far as Gimp is concerned it sounds inconsistent not to be able to properly
read again a file it has written itself..."
(See also comment 10 in Bug 676219)

I have submitted a patch with Jigebren's suggested changes to this bug report.