Can two comets travel together as one? If two comets come together in space, will they bounce apart, merge into a single body, or could they travel together through space, either touching or orbiting a shared center of gravity?
Yes, binary comets do exist; 8P/Tuttle is an example of one. This is an area that is still being heavily researched, but it is suspected that binary comets can "form from collision, mutual capture, or fission."

In recent news, the comet 67P/Churyumov-Gerasimenko has also been revealed to be a contact-binary by the European Space Agency's Rosetta spacecraft.

Sources:


Radar observations of 8P/Tuttle: A contact-binary comet - Harmon, Nolan, Giorgini, Howell
Rosetta's target is 'double' comet - BBC