I am afraid at 01:30, there will be no scheduled airport buses at IST
. The HAVAS bus (the airport shuttle) website says that after 01:00, they will have extra services to the city center depending on demand. But I have a feeling you should be lucky because there are quite a few flights arriving at that time of the night.
Otherwise, you will have to wait until 04:00 AM
for the first bus to the city center and from there you can connect to the bus to SAW
and you will be at SAW
at 06:30 AM
. (cost 9 YTL approx. 5 Euros)
The HAVAS bus runs from IST
to city center between 04:00 AM
and 01:00 AM
every half an hour. And the bus to SAW
from the city center runs every hour between 03:30 AM
and 24:00 hrs. (cost: 9,5 YTL and again approx Euros)
A taxi at that hour to the city center should normally cost around 50 YTL which is about 30 Euros. You would then have to wait for about 1 hr and a half for the connecting bus and I think there are no waiting lounges in the city center office.
I hope this helps despite the bad news.