You are mixing apples and oranges. Create a partition table on
/dev/sdb and copy
sdb1, or copy all of
sda (partition table and all) to
I can report success with the former, albeit my experience is from many years ago; but the latter is tricky to get to work entirely correctly. Perhaps you're better off creating a partition table and installing Grub separately. There are various recipes for making USB sticks bootable; it's not hard.
I'm rather confident the latter will not work unless you can set up
sdb to have exactly the same disk geometries etc; or limit the
dd transfer with something like
bs=1024 count=33554432 (probably better with a bigger block size and a correspondingly smaller count), and live with the fact that the partition table is not exactly right. If you mount the boot partition read-only, you should not be able to create any damage to the file system anyway (... I hope).
As a partial workaround, if you can play around with the disk on your source machine, you could set it up to have two partitions in the first 32G and then mount the rest as a separate
/home partition or whatever; then maybe live with the fact that the stick will try to mount a nonexistent partition (maybe that will kill it, haven't tried).