If you have an Oyster card you can either buy advance credit - in which case the fare is £1 - or you can buy a season ticket - in which case the incremental cost of your journey is likely to be zero. Of course, if you have already travelled on your oyster during the day then you may not have to pay extra because the fares are capped at a maximum of £3.30 for bus. That is unless you are combining with tube journeys in which case it depends how many zones you have travelled through. Always assuming that you remember to "touch in and touch out" otherwise you may end up paying for the maximum fare possible - particularly relevant if you make journeys that include those segments of the transport system that due to privatisation are run by companies not in the Oyster system. If you pay cash you need to buy the ticket before boarding which will cost you £2 for each journey, unless you realise that the daily bus ticket is £3.80. Of course, if it is a bendy bus you could do the same as a large number of unscrupulous locals do and travel without paying.
Makes you proud to be a Londoner.
Or you could go by bike ;-)