My husband and I would like to arrive to London in mid September and depart Shannon two weeks later. We have not visited England or Ireland or Scotland previously so I am seeking advice regarding itinerary and best methods of travel and recommended housing accommodations. We are physically fit and enjoy historical, gardens, and food. We plan to travel via bus and train but are not opposed to flying between cities if that is best utilization of our time. Perhaps should use local tour company if recommended. BB accommodations or apartment rental are great also. My husband would like to see some of Scotland but I feel that should be another trip. Or should we drop Ireland and focus on UK?
With your timeline, I'd choose either England and Ireland OR England and Scotland. Just not enough time to do all three.
With only two weeks I agree with Toni, don't try to "squeeze" in Scotland on this trip.
I'd suggest focusing your England time in London, with day trips to places like Hampton Court and Kew Gardens, and maybe an overnight by train to York. In the time you have you won't want to spend a lot of it in transit. London has ample history and beauty to fill a week or even two, and the day trips can get you to some good gardens (not my thing really though). Oxford or Cambridge (not both) might be another day trip.
Then I'd say fly to Dublin or Shannon for the Ireland part of your trip. I haven't been there but what I've heard is that a car is needed to really appreciate the country. Maybe some time in Dublin and some kind of guided tour elsewhere if you don't want to drive.
You're wise to be flying open-jaw given the length of the trip and the distance you want to cover. Don't try to do too much -- assume you'll return.
I've done the England and Ireland combo but it was ONLY London and then all of Ireland AND N. Ireland. I would save Scotland for a separate trip or Ireland as a separate trip. Keep in mind in Scotland and Eire having a rental is in my HMO the best and ONLY way to enjoy each country to it's fullest. Provides a freedom that buses and trains can't. Obviously you could also concentrate solely on England and explore the Cotswolds, or the Lake District or the seaside and combine those days with the every changing but always same London. Just calculate transport time into your travel equations.
As far as BB accommodations take a look at Airbnb, or At Home in London. Rule(s) of thumb for Airbnb (which I use all the time to find my accommodations) is that the owner of the property being offered has their image, not their dog's or Big Ben, or the Queen's image on the profile, that there are a minimum of 10 positives reviews and if you contact them they contact you within 12 hours. Finally they also answer all of your questions to your satisfaction, are there stairs, is there wifi, how is the property heated, what's the closest tube stop, ATM, etc.. I'm staying at a flat this November, booked months ago and the owner and I have established a nice email correspondence. She's even provided a map of her favorite dining spots in the neighborhood.
If you choose to stay in London, great day trips via public transport are Hampton Court, Bath, Oxford. Kew Gardens would obviously be on your itinerary but also consider these spots. Chelsea Psychic Gardens and the gardens at Syon House and Park. The latter is close to Kew Gardens.
Lastly, talk a look at London Walks (www.walks.com) and see if any strike your interest. Lovely way to see and learn about parts of London and surrounding environs. Enjoy your trip.