I think the Apostles did teach the basics of the faith, not over months, but they certainly talked about the faith for some time before the Baptisms. In St. Paul's epistle's he says to keep everything they've received from him whether by word or letter. So it seems like he taught them the basics before baptism, and afterwards he's writting to continue their education.
In my Church we don't bother with the form catechism program any more because of the low volume of converts. I was never a form catecumen. I just went & talked with my priest until we were both satisfied that I was ready, and then he baptised me. For me that took about 8 months, but for a friend of mine who wasn't set in another tradition beforehand like me, and who could spare more time to talk to our priest more frequently, it only took about 2 months. It took him some time to sort out the differences & get rid of the wrong elements of his United upbringing. The people in the NT didn't have any wrong Christian teachings, they were receiving Christianity as a new thing, so there were none of these little details to get into. So it seems to make sense that it took less time, and they could be Baptised after the basics of Christianity were explained to them, perhaps even in only a day's preaching. Later, when there was a lot of disputing in Christianity, there was more time needed to teach. Also, we see that the early Church fell into a lot of errors, which the Apostles wrote epistles & viisted to correct. Later when the Church was more established, there was no need for the bishops to baptise quickly and move on as St. Paul and the others did, it was possible to take more time and teach more fully to avoid these problems to begin with, so that's what happened. Now there's not the big controversies in the Church, it's obivous where Orthodoxy is, and there aren't Arians and Nestorians running around claiming to be the Orthodox Church, so it's a little easier and it's not so necessary to have long and formal periods of catechisis.