Bursiform probably is the root of the term Burse, a
cloth covered square cardboard container. It held the
Corporal, a square cloth placed in the center of the
altar, on which the sacramental bread and wine were
placed. Theoretically only the bread and wine on the
corporal were consecrated as sacred species, at least
in the old Roman Church. They watered so much down
it probably does not exist there any more. At any
rate, when not in use it was contained in the burse.
The corporal was washed in a sink called the sacrarium,
which emptied directly into the ground not a sewage
outlet, so the sacred species, bread crumbs,i.e., would
return to the ground whence grew the wheat.

English purse < Late Latin bursa 'purse, pouch' < Greek bursa 'ox hide; skin'. Bursar and burse both come from the Latin term. I'm pretty sure the rules about the burse and the corporal are still pretty much as they used to be.

Could be. I just have not seen either in years when I am
in a Roman Church.