Is there a way to have Mate on a jump drive in both, 64 and 32 bit versions so I am able to preview on someones computer and then install the proper version according to their system specs?
Yes, basically you set up a 32-bit partition and a 64-bit partition, then boot from the one you want. Suggest making them both “primary” partitions if you’re using a msdos partition table, some bios-firmware plays hard-rules and will bellyache (at least) if you try to boot from an extended partition.