[Hampshire] Convert 8-bit .bmp to 32 bit

This should be trivial, but I'm struggling to do it.

I have a few 8-bit .bmp files that I want to convert to 32 bit. I realise
they won't look any different... I have tried:

$ file x.bmp
x.bmp: PC bitmap, Windows 3.x format, 22 x 22 x 8
$ convert x.bmp -depth 32 y.bmp
$ file y.bmp
y.bmp: PC bitmap, Windows 3.x format, 22 x 22 x 8
$

I've looked at the gimp, but can't see how to do this. I've googled, but
"32 bit" is an unfortunate phrase to include in a search.

I plead graphic-ignorance: can someone help me out?

Thanks,
Keith