Your situation seems to involve quite a bit of back and forth between Northern Ireland and London, along with potential relocation. While I don't have specific information on which bus card would be best for your needs in London, I recommend looking into options that offer flexibility and coverage for different modes of transportation. One option is the Oyster card, which is widely used for accessing London's public transportation network, including the subway, buses, and some trains. However, for personalized advice, I recommend contacting Transport for London directly.