So I went to the British Museum and they had an exhibition of British propaganda prints and drawings from the Napoleonic era. I noticed that already by that point they were using speech bubbles to indicate who is speaking (although they didn't have a white background for the bubble, must be a more recent development). When and where did speech bubbles become common in denoting who is speaking and what?
Speech scrolls were used in Mesoamerica since around 650 BCE. One of the earliest examples is a the San Andrés cylinder seal which depicts a bird speaking the name of a ruler.
In Europe, speech scrolls have been commonly used since the 1300's. The earlier examples show sentences connected to people's mouths with lines, whereas later ones have them written on little scrolls.