may do better heading towards SE London - it doesn't have the underground, but has plenty of proper trains - a lot of the stations in the general direction of blackheath / greenwich have trains every 10 minutes to central london (mainly charing cross or london bridge (change for charing cross) / cannon street, but some do have direct trains to victoria as well) - and as they don't stop as often, a journey from (say) zone 4 to central london is a lot quicker by real train than a similar distance by underground.
having mum-tat in SE London, i've never stayed in any so can't offer direct recommendations. from what i gather, there's plenty of places in london that work on the basis there's so many tourists passing through london that they don't care a great deal about repeat business...
or as ex services, would it be worth contemplating the union jack club at waterloo? again can't offer any personal thoughts.
another couple of things that may or may not be stating the bleeding obvious - if you have a scottish concessionary bus pass, you can't use this for travel in London - 'national' in this context means the 4 countries of the UK.
and you can't pay cash fares on buses in London any more - you can either pay with a contactless card, get an Oyster Card, or do a 'one day travelcard' each day - this covers all TFL bus services (pretty much anything except the open top sightseeing tour things), underground, overground rail, national rail services, Docklands Light Railway and (should you really want to venture there) the Croydon trams. You also get a discount on the Thames river boat services.
