Tickets
There is variety of ticket available for public transport in Budapest. Daily, weekly, for 5 days within a month etc. Check out which is the best option for you on the website of Bupdapest Public Transport (BKK).
The best way to buy tickets is to find one of the „BKK Automata” you will see in this map where they are. There are plenty of them, so it will not be difficult to find one.

There are ticket vending machines at the Airport and at every train station, at most of the Metro stops and at many other locations.
The closest ticket vending machine to Bölcső7 is at the Metro stop „Újbuda központ”. Only 4 minutes from the apartment.

Night Service
Night service works pretty well in Budapest. It will not be difficult to get back to Bölcső7 even if you do not want to travel by taxi.
The best way to plan your night trip back to Bölcső7 is to use Google Maps to plan.