Heathrow to Premier Inn in Southwark

I'd take the Elizabeth Line. Like you say, it's six and half a dozen really, but the Elizabeth Line is much nicer than the rattly old Piccadilly Line trains. I can't remember what the transfer from Jubilee Line to Piccadilly Line at Green Park is like. Is that the one where it's a bit of pain? I seem to remember a shortcut is leaving the station and going back in again to avoid a long walk underground?

Borough High Street is a good spot to stay in my book. Bit of character away from the glitz of the west end but still plenty of interest around.

Don’t use Rome 2 Rio. The route it gave you for option 1 doesn’t make sense. Also, Sept 6 was yesterday. Did you mean to check for Fri, Sept 13th?

Option 1 has you taking the Heathrow Express to Paddington and then changing to the Elizabeth line. That makes no sense unless there is some kind of partial closure on the Elizabeth line. You can take the Elizabeth line from Heathrow to Bond St and make one change to the Jubilee line.

I agree with Gerry about taking the Elizabeth line. You can check the route for your day of travel using the the TFL website’s journey planner.
https://tfl.gov.uk/plan-a-journey/

I came back to say what Laura just said when it clicked with me that Rome2Rio was suggesting taking the Heathrow Express to Paddington. Wut? lol Take the Elizabeth Line to Bond Street from Heathrow and change there for London Bridge. Easy peasy. Rome2Rio is hopeless :)

As Laura mentioned, for journeys inside London, use the TfL site they linked to. The results from a simple Google search such as "Heathrow to London Bridge" is going to give a few options you can weigh up too.

As with almost every journey in London, there's several different ways to do it depending on your mood, how long it's going to take and the mode of transport you prefer. I don't always go the fastest route. Once you're in London a while the most fun / least crowded / most relaxing is something you start to base these decisions on, but that takes time and experience.

If you have a smartphone, I'd suggest downloading the Citymapper app. It gives more options for travel in London than the official TFL Journey Planner as well as current status.

Yes, I meant Fri the 13th (a lucky day in my family history) - I guess I'm eager to be there already.
I remembered from earlier planning and forum browsing not to trust Rome2Rio, but had forgotten about the tfl site, which seems a MAJOR oversight. It's crunch time and I need to get my act together! Thank you, Gerry & Laura!

In my experience Rome2Rio works well to show you alternatives on long trips. I used it to find a route from Copenhagen to Leicester, UK. It gave me routes I would never have thought of myself.

For local trips I - like most above - would use a local source, like TfL.

The TfL app also gives you current status (and live timings/fastest routes etc)- of course it does, they are the operator. Any other app derives it's data from TfL, it just presents it differently.

London Bridge station has multiple exits. Citymapper will tell you which one to use and that will cut down your walking time significantly. The PI is very close to the station if you use the right exit.