Its about 4 miles to walk, Sandy has the wrong station in his link. Another option if you're happy to walk part way for example, is to walking to Waterloo along the southbank and catch the 139 bus up to Marylebone. No change needed. Here's the bus map with the key routess if you want to look at the options...
Here you go...https://www.google.co.uk/search?q=directions+london+bridge+to+bendall+mews&oq=directions+london+bridge+to+bendall+mews&aqs=chrome..69i57.27468j0j4&client=tablet-android-google&sourceid=chrome-mobile&ie=UTF-8
Walk from London Bridge Station to Borough High Street,
catch the number 17 to Caledonian Road
Change there to number 274 bus to Baker Street Station
Walk from Baker Street station to your Mews address
Its about 4 miles to walk, Sandy has the wrong station in his link. Another option if you're happy to walk part way for example, is to walking to Waterloo along the southbank and catch the 139 bus up to Marylebone. No change needed.
Here's the bus map with the key routess if you want to look at the options