Hi and welcome to the UK.
I have been to Bicester many years ago.. nice part of the country.. not far from Oxford and all that holds of interest re history/shops etc...
I hope you find some fellow compatriots in the area and I am sure in time you will.

In the meantime, keep in touch with your new American (and Welsh) online friends here to keep the lines of communication open and your sense of belonging. Your dogs will help you in making new friends as people who walk dogs generally get to chat at some point on the walks. Sometimes English people (not representative of all of the UK inhabitants though I hasten to add) are not very chatty to begin with, the old reserved attitude can prove to be prohibitive when making new friends, don't be put off by this.. sometimes it is merely shyness and has nothing to do with them not wanting to chat to you.. be brave and be the first to break the ice! You may just make a new lifelong friend.

We were very fortunate when we moved to Michigan in the 60's as the apartment complex we lived on, had other ex pats from various parts of the world.. we had English, Japanese, German, Russian, Swiss, Greek/French Canadian, Cherokee as well as many wonderful American friends.. still in touch with two close friends from Elementary School there.
Enjoy the upcoming weather.. its going to be about the best we have had this year!!