Thanks, Laura. We made it, with some fortunate karma from a red-headed traveler who heard me asking about the Nbr. 8 bus at the airport! I'll post the answer, for anyone else taking this route.
The only bus (that we spotted) from DBV is the airport connection bus. It costs 40kn (or 6 euro) pp, cash only. The first stop is the Pile Gate, which you do NOT want if connecting to the city bus. Continue on to the 2nd stop, which is Dubrovnik's central bus station. From there we were able to catch the Nbr. 8 local bus (or any of many others). It runs about every 10 minutes, from bus-bay #1.
Oddly, the lady at the ticket window would not sell us tickets (which, apparently, would have been 12kn purchased from her). She said to buy the tickets on the bus from the driver, and she also said the driver would give change (which was not the case). The bus tickets, from the driver, were 15kn pp. We showed the driver our printed Google map (route to our apt.) and he nicely announced the stop at the "Bikers' Cafe."
No, we aren't 'bikers'!! Yes, there actually were some serious looking bikers present (one had a jacket reading "Hell's Angels Australia" - quite the ride!). According to our host, many of the tour operators use the Bikers' Cafe as the pickup point, so it is fairly well known locally.