Certainly, there was nothing preventing a skilled individual from making use of a bow and arrow. Some Native Americans, for example, continued to employ both bow-and-arrow and guns into the late 19th century.

The trick is the skilled part of the equation. A proficient bowman takes substantially longer to train than a proficient musketeer. Operating a bow at peak efficiency took years of exercise and practice. Meanwhile, a soldier with the basic physical capacity to swing a musket around could be taught to fire three rounds per minute with usually only a few weeks/months of steady training.

Making a bow is also something of an artform, requiring a feel for the bow wood as craftsmen select wood and slowly bend it into shape. As such, it was difficult for cultures who had switched to firearms to return to making bows on a military scale. The Iroquois found this out within a generation of contact with Europeans: in the great rush to adopt firearms, a generation of young men failed to learn how to craft bows from their forebearers, and the number of successful bowmakers sharply decreased.

Ben Franklin toyed with the idea of equipping the Continental Army with bows, but nothing appears to have ever come of it. Presumably, the fact that few, if any, people in the United States had ever made or used a bow help dissuade him

I don't know of any examples pitting musketeers against a Roman-style shield wall, which probably tells you how impractical an idea that is. It would be extremely difficult for a soldier to carry a shield heavy enough to stop a musket ball and any kind of weapon, particularly one with enough range to fight back against a formation of musket-wielding opponents. Some of the British battles against the Zulu might count as musket v. shield wall, though I am not an expert on those conflicts.

Sources

https://allthingsliberty.com/2013/09/bows-and-arrows-pikes-and-spears/

Martin and Galaathar, Forgotten Allies.