"Pike and shot" is a very specific term referring to the use of pikes and firearms together. As a turn of phrase, it did not exist before the Italian Wars circa 1490. While pikes and muscle powered ranged weapons being used together go back further than Roman times, nobody called that "pike and shot". "Shot" refers specifically to stuff coming out of a firearm's barrel.
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Most major continental European armies had phased out the bow and arrow in the 1500s. Rosters of the Army of Flanders from 1567 do not mention bowmen at all. It was already recognized that firearms were vastly superior.
English, Scot and Irish militaries should not be far behind in this realization, small numbers of them regularly campaigned on the continent as mercenaries or adventurers. So a bowman given an upgrade to firearms should be quite glad to be given the facility. Going back a bit in time, even Henry VIII Tudor was already aware of the reforms undertaken by the armies of Charles V as they transitioned away from bows to firearms. By 1560 there were already about an equal number of firearms and bow among the shot footmen; by 1595 the bow was no longer considered acceptable for a first-line formation.
This is not to say that the bow completely disappeared, first we have to note that there was not yet one singular "state army" and therefore we have a variety of armies from the first-line troops to the local militia, who did keep various bows for longer. They were simply no longer a factor in non-trivial engagements.
The decline of bowmen was rather quick. At the start of English intervention on behalf of Protestant Scotland, it was reported the ratio of footmen were roughly equal between pikes, bills, longbows, and calivers (a type of small arquebus). The bills were discarded and replaced with halberds immediately. The longbows were replaced by others, according what was available. By 1595, longbowmen were categorized among unarmed men.
Pike and shot tactics changed a lot over the 200 years that firearms and pikes were used together on the battlefield, but the transition from bows and crossbows to firearms didn't change how things were done initially.
In the early 15th century, armies traditionally divide their pikes into three sections: the "forward", the "main battaile" and the "rearward". The missile weapons would then take their place either on the wings or in the very front, where they were known as the "forlorn hope". Bows, crossbows and firearms probably all coexisted here for a time before the firearms took over completely. The military writer Raimond Fourquevaux was advocating for armies to keep a small proportion of bows and crossbows as late as 1548.
In this illustration of the battle of Pinkie Cleugh you can see how each of the armies has divided their pikes into three blocks, and the English army, top, has sleeves of harquebusiers on the wings. http://imgur.com/ARXaITE