No, if you come out of the Bonjour into the square, turn right and walk up to the main road. Turn right again and keep walking for a couple of hundred yards or so - Tansas is on the other side of the road, and the bakery is round the corner from it. Just a five minute walk at the most, I'd say.
Fantastic bread and if you ask they will slice it for you, saves hacking at it with a blunt knife in the apartments. Tansas do a fantastic salami with pestacios which goes fantastically well with the bread and an Efes on the balcony.
Not sure about the bakeries, but most of the restaurants will happily provide a birthday cake for you, providing you give them at least a day's notice. Most will put up balloons, etc, for you as well. Just pop in at least the day before and tell them you want to book for a birthday (or similar celebrations, like anniversaries) and they will do you proud!