I'm English so maybe we use words differently, but all I know is that if I saw a jar on the supermarket shelf that said-
"INGREDIENTS FROM THE HUMBLE BEE"
or "INGREDIENTS OF THE HUMBLE BEE",
I'd think "What the heck, are there bits of bees bodies in it, and what is a Humble bee anyway?", and I'd put it back on the shelf.
But if it said "INGREDIENTS PRODUCED BY THE BUMBLE BEE", that'd tell me exactly what I need to know, and I'd buy a few jars..