Trailer, for sure. A kids type will work, but one designed for pets (flat floor) will be better. As stated above, it's better to start exposing your pup to new experiences earlier rather than later. If the furbaby isn't thrilled with the idea of riding in a trailer, start slowly, like just getting in and out without moving. Then after learning it's safe inside, you can roll the trailer (by hand) across the yard a bit. Eventually, make slow progress until being towed behind the bike is no big deal.
-Kedosto