Judith Martin, aka Miss Manners, lives RIGHT THERE in Washington D.C. They should ask for guidance. A gift to royalty shouldn't be like a Christmas gift to your relative. It's not like she needs more junk in the castle. It should be symbolic. My idea would have been to plant a rose bush in her honor in the WH rose garden, with a plaque saying so, and give her a picture of that. Dumb? Too cheap?
Anyway, gifting back the bust of Churchill, is the best answer so far (from page 1 Brit comments). 
I'm not so sure that Miss Manners is the right expert in this particular department. Sure, if I want to give a party or want to entertain, she's the one I'd ask if the small fork goes on the left or the right or up top of the table setting.
But we're talking about
British tradition and
British diplomacy vis-a-vis the monarchy. That's a different world altogether, I would think.
Jendf earlier asked in her list if there was some other kind of diplomatic gaffe she might've missed. The bust of Churchill debacle comes to mind. That one was outrageous, in my opinion. Even if His Holiness didn't want the bust in the Oval Orifice, he didn't have to give it back to PM Brown. That's just plain rude.