A lot depends on your viewpoint.
In the US, there were very few Catholics, prior to the Revolutionary War. Those Catholics that WERE in the US then, were widely scattered across a huge continent. Technically, Colonial American Catholics were under the jurisdiction of Bishop Challoner, who, as is commonly known, published a revised English Translation of the Bible, several times during his own lifetime. Colonial Catholics, who had very rare opportunities of seeing a priest and receiving the Sacraments, depended entirely on their Catholic Bible to sustain their Faith. In the large cities like Philadelphia, where it was ok to practice Catholicism, the Jesuits were the predominant Catholic clergy. After the Revolutionary War, the Jesuit Priest John Caroll was installed in Philadelphia as the first Bishop of the US. About the same time, Mathew Carey printed the first Catholic US Bible in 1790. This was remarkable, as the first Protestant Bibles to appear in the US just a year earlier, required subsidies from the US Congress to pull off. By contrast, the tiny US Catholic Community printed their own Bible without any Government help. By 1825, Eugene Cummiskey of Philadelphia was printing small Octavo Catholic Bibles, Quarto ones, and even a complete reprint of the Famous Haydock Folio Bible of 1811. From that time forward, there were PLENTY of Catholic Bibles in the US for every kind of Catholic, whether rich or poor.
So (at least here in the US) the Catholic laity, almost from the earliest days, commonly had a Catholic Bible.
In England, we can even say that the better off Catholic laity had Catholic Bibles going back to the original Douay/Rheims Bible. Bibles in Elizabethan England were not cheap however, not even for Protestants. So the poor persecuted Catholics had a far more difficult time of getting possession of a Catholic Bible. Still, it would not be wrong to say that English speaking laity commonly had a Catholic Bible (assuming it was within their means.) But by Bishop Challoner’s time, with his small 12mo Bibles, which were relatively cheap, most Catholics had Catholic Bibles. From his time forward, the cost of Catholic Bibles decreased, and the number of cheap printings continued to increase in the UK.
English speaking countries are a special case. But in the rest of Continental Europe, Catholic Bibles in the Vernacular appeared earlier, more frequently, and cheaper.