It depends; ideally modules mucking about as Wx::Bitmap seems to would provide Storable hooks to be properly serializable
Nice, I'd missed/forgotten about those hooks. I don't think it'll work for Wx objects that are subclasses of Wx::Window. But it'd probably work fine for Wx::Bitmap. Here's some untested code for (de)?serialising Wx::Bitmaps...
my $bitmap_data = $wx_bitmap->GetImage->GetData;
# serialise bitmap data
$wx_bitmap = new Wx::Image()->SetData($bitmap_data)->GetBitmap;