It was very much something that East Berliners could, and did, do from the end of the war up until the construction of the Berlin Wall. It was less common, but West Berliners did the same thing and worked in the East. In terms of how common it was, it was a very normative thing that was understood as part of Berlin being a divided city. While I don't have statistics for the whole time period, Hope Harrison in Driving the Soviets up the Wall provides a number of 50,000 East Berliners working in the West in 1960.

Despite the opposition of the leadership of the German Democratic Republic (GDR) to East Berliners working in the West there were no laws or policies explicitly prohibiting it. It is important to also note that the biggest concern was not so much people working in West Berlin, but rather the use of West Berlin as a means to flee to West Germany.

In terms of things changing the biggest factor is via currency reform in East Germany in 1957. This move replaced all Ostmarks (East German currency) printed between 1949 and 1957 with new ones. The shift altered the economic flow between both sides of the city, as West Berlin businesses were unable to exchange their Ostmarks and drastically decreased purchasing on both sides of the city from citizens on the other side. This also coincided with a new passport policy on the part of the GDR which radically changed the movement of people from East to West Germany and made West Berlin the primary site of flight from East Germany to West Germany.

As this would apply to workers it would be more incentives for a worker post-currency reform to either fully leave to the West or to work in the East. However, up until the literal day the wall began construction people were commuting both ways to work while living on the opposite side of the city. So in terms of actually working in West Berlin while living in East Berlin the big change was the currency reform alongside the overall governmental shift to one of completely severing free movement to West Berlin.

It is not the easiest to track down, but the 1952 East German film Frauenschicksale (Destinies of Women) has as a central theme people working in West Berlin while living in East Berlin. It calls into question how committed those who do so are to the East German socialist project, and portrays those in the West as greedy users of East German women. That being said, it is an insightful movie from the period both in terms of what life in Berlin looked like in 1952 and about the opportunities that could exist for people to work in the West and live in the East.