Okay so for a time there was a theory that most maritime trade was basically this process of traders sorta just working their way along coastlines looking for a profit wherever they could. The idea was that Greek merchants didn’t really have set ideas of where there was a good market for anything so they just bought and sold whatever and wherever they could.

Nowadays, we know that is not true. Merchants in the ancient world actually had a very complex understanding of the wider market and where they could make a profit. As such, they plied specific routes, often over rather large distances, that they knew would make a profit.

For your question, the answer is that it kinda varies. Strabo tells us that, under the Ptolemies, some 20 ships made the journey to India each year which increased to 100 under the Romans. Now whether or not we accept those exact numbers, the point is that he attests to a certain number of Greek and Roman ships making the journey as far as India each year.

However, there are a couple of points to raise here. Firstly, there is no reason to suspect they personally went any further east than India (it just wouldn’t make any financial or personal sense to do so). Secondly, these Greeks and Romans are probably a minority of shipping.

Instead, the main journeys across the Indian Ocean were probably dominated by the Arabians and Ethiopians (specifically Axum) who understood the winds of the Indian Ocean a lot better than the Greeks. That said we do hear of attempts by Ptolemaic explorers to try and map the winds in the later periods of the dynasty.

So for the Greeks and Romans, trade in the Indian Ocean was probably mostly through intermediaries (buying and selling at, say Adulis or Muscat or Petra). However, plenty of Africans and Arabians were making direct trips across the ocean.