Hostess gift

Unless the B&B host is letting you stay there free of charge, there is no reason at all to bring a gift.
Just be gracious and polite guests and leave them a good review. Nothing more is needed.

A hostess gift would be appropriate for a stay in a private home, but this is not that. The B&B is being run as a business and is being rented to you on that basis. I have no doubt the person managing the B&B has an ample supply of tea towels. They may even own a dishwasher!. Instead, leave a favorable review after your stay, if it is merited.

I agree with Dutch Traveler; do not bring a gift from your hometown. A good review following your stay would be appreciated more.

I disagree. I think something from Oklahoma would make a very nice gift. Perhaps a small folk art or craft made by a Native American artisan. It’s more about sharing something that’s unique to a culture than monetary value or practical use. Good luck with the trip!

I agree with Johnt. You had a kind thought, don't be put off from following it through! Anything with an Oklahoma theme would be fine, and a tea towel is always useful!

I stayed in a B&B in Ireland where regulars brought small souvenirs for the hosts that fit with their business name. I thought it was a nice gesture and would take something for them if I went back. I think some souvenir of Oklahoma would be a nice.

It's hard to tell without knowing the place. If the person is renting out their family home and is very involved in planning and your stay then a gift is absolutely appropriate, but if it's simply a business enterprise run by absentee owners then there's no point. Without knowing more taking a small gift that doesn't take up much space is a good hedge against having a wonderful experience and having no gift.

Italians are also fans of super local produce like honey or very specific food items as long as they are organic and of known origin. Pride in local ingredients is something Italians understand because each region and even each town has their own "things" they are proud of. (Of course check import restrictions for personal use but processed agricultural products - not raw vegetables or plants - that don't involve meat are generally allowed.)

My $.02,
=Tod

If you think of giving flowers, avoid chrysanthemums --- they have a connotation of cemeteries and death that they don't have in the US. I am less sure about the meaning of cyclamen and white lilies in Italy, but they might also have similar associations --- at least, I often see them grouped with the chrysanthemums in flower shops and being sold near cemeteries.

If you’d like to express your appreciation this way, then do!

I was in a roughly similar situation, wanted to thank my Italian rental agent for going “above and beyond” during my month-long stay. I gave her an artisan bottle opener that I had bought at an art museum gift shop back home. She loved it.