The hop on hop off tour buses are not worth the time, effort and cost nor the best way to fight jet lag.
Once you get settled at your accomodation and have your Oyster card, get on the tube ( Victoria Line) to Green Park. Mind the Gap, Exit. Switch to Jubilee Line train to Westminster.
Westminster is the tube station for Parliament Square.
Elizabeth’s Tower, Big Ben ( under scaffolding ) Parliament, Westminster Abbey. Walk around, get your bearings and then walk up Whitehall past the HorseGuards to Trafalgar Square.
Have you first pint at the Ship and Shovell which is in the Craven passage or the Sherlock Pub. Both within easy walking distance of Trafalgar Square.
After your respite walk along the Thames. You’ll see the London Eye across the river. Good first few hours
Of introduction learning about the tube, and adjusting to the sites and sounds of London. A second walking option from Parliament Square is to follow Birdcage Walk through St James Park up to Buckingham Palace. As you’ve indicated you want to see the Changing of the Guard you can preview the area and figure out where you’d like to stand.
As you are traveling at the height of tourist season yes arrive early for the Tower of London and go straight to the Crown Jewels. Westminster Abbey will a zoo so go later in the day. 3 or 4 hopefully the hordes will have thinned out.
Pre book Churchill War Rooms. Massively popular due to The Darkest Hour. Even with pre booked times tickets you will still have to queue ( line up ).
I’m not familiar with the London Bridge Experience
( in fact I thought London Bridge existed in Lake Havasu AZ) I do know the Tower Bridge Exhibition, not for those with fear of heights. http://www.towerbridge.org.uk
Sunday Markets close to Tower Bridge experience would be Brick Lane, ( loads of eye candy and food stalls), nearby Spittafield’s, Borough Market (now trendy, no longer grungy ) or the Maltby Street Market which started in 2010. I’d opt for Brick Lane and Spittafields.
You should also consider booking a traditional Sunday Roast pub dinner near where you are staying.
If you must see the Changing of the Guards then go. Crowds will be huge,but go early to secure a good POV or you will see nothing but backs of people’s heads.
You can see more of London with your itinerary.
After seeing the Churchill War Rooms you could easily visit the adjacent Horse Guards Museum.
After seeing the Tower of London easy walk to the glass covered Leadenhall Market.
Museum of London should be added simply because it provides history on how the city you will be exploring came to be London. Free and well done.
Walking in Hyde Park and Kensington Gardens is always pleasant in good weather. Lots of dog walkers. Might even see the Royal Guards Horsemen practicing. Waterfowl ( swans, geese, ducks) as well. Even green parrots by Kensington Palace.
Lastly use google maps satellite view and plot out your itinerary. You’ll see you’ve combined places not close to one another. Yes with Oyster you’ll be able to get to all places BUT would make far more sense to group places that are closer i.e. Westminster Abbey, Churchill War Rooms and London Eye.
Great city have fun!