When did Orthodox Christians (normal citizens, not clergy) get access to the Bible?

I am not aware of any Orthodox ban on laypeople buying bibles, if they could afford them. It may or may not have been seen as odd before the invention of printing.

The Greek Orthodox Church did have a massive problem with translating the Bible into Modern Greek, to the extent of getting a ban on translations written into the Greek constitution. It has been possible for laypeople to buy translations since 1638 (Bible translations into Greek); but the church of Greece seems to have only officially signed off on translations since the 1990s.

The resistance was more about fetishising the source language than about wanting the great unwashed to gain access to the original. The uproar around Ioannikios Kartanos’ paraphrase of the Bible in 1536 seems likewise to have been more about the fact that he used an Italian source text with a lot of apocryphal interpolations. But the Orthodox church was certainly no fan of people making up their own minds about how to make sense of the Bible.