I still can’t wrap my head around saying Italian eye-talian, yet all over Michigan they say it that way.
I was going to say what @jca2 just said, you need the double consonant in Biden to pronounce it Bid-den in English, but of course with names and words in English you can do whatever you want in the end.
Race car driver Rafael Matos (we used to spend time with him years ago) was very frustrated when he first started racing professionally that announcers said his name may-toes. I told him if it was spelled Mattos they would more likely get it right. That doesn’t compute in Spanish and Portuguese though. For those languages the a is always the same.
Bidet is French, as @kritper said, and I guess we kept the French pronunciation. Just like we say Cartier cart-ee-ae.