What to say to someone who is going to eat

Speaking as an Iowan now living in California, I would simply say, "Enjoy."

The intransitive use of 'enjoy' is now fairly extensively used by restaurant staff in Britain too.

I agree with the OP that English greatly lacks a suitable term for enjoining your dining partners in the way that 'bon appetit' does in French.

But English, across the centuries, has overcome natural deficiencies, by simply borrowing a foreign expression. Are there really many people in America who wouldn't understand what 'bon appetit' meant? I alternate it with 'Guten appetit'. But doesn't Spanish have an equivalent which Americans might use?