Captioned speech, if you like, exists in political woodcuts and engravings as far back as the 17th century. (I'm not aware of earlier examples, but others may be). If you look at this woodcut from 1665, which comments on the outbreak of plague in London that year, you see that there are instances of text in the image which are clearly meant to be understood as speech from the figures depicted: http://www.alamy.com/stock-photo-plague-of-london-1665-nlord-have-mercy-on-london-contemporary-english-95443792.html

Obviously, these aren't delineated as speech 'bubbles', but the effect is the same. In Anglophone print culture, at least, the speech bubble seems to have been a development of the mid-18th century. You can see it in political cartoons such as these: http://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=3076432&partId=1&searchText=pitt&images=true&from=ad&fromDate=1740&to=ad&toDate=1765&page=1 and http://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=3074722&partId=1&searchText=pitt&images=true&from=ad&fromDate=1740&to=ad&toDate=1765&page=1

The speech bubble developed in political cartoons because these images were dealing with fairly complex events, not always easily reducible to a single trope or caricature. They enabled satirists - who occupied a ground somewhere between news reportage and propaganda - to put words in the mouths of political figures, providing both exegesis/exposition of the context, and exposure of a political figure's true actions or motives.