Christianity actually spread very quickly throughout the Roman known world. With Jesus crucified 36AD (with 12 followers and maybe 500 believers), 320 years later (380AD) the whole Roman empire was officially Christian, the Christian clergy was 100,000 and there were maybe 30 million believers throughout all the Roman world and beyond.
Jewish people did not spread Christianity at all, they were not Christians and diametrically opposed to Christianity from 60-70AD on. Of course Christianity did spread among Jewish communities as Jewish people converted, but Jews did not 'spread Christianity'.
In terms of the Jewish Diaspora there were '3' Jewish- Roman wars...1st 67-70AD, Kitos war 115-117AD, Bar Kokhba war 132-36. the Jews lost all 3...really bad, they were slaughtered by the Romans. By the end of the last one (136AD) there were hardly any living Jews left. The last 2 wars were fought by the Jews under false Messiahs, so they weren't doing it for Christ. The very few Jewish survivors were spread throughout Europe, North Africa, Mideast, they did not spread Christianity or anything else being too few and dispersed.
*Jesus, his disciples, all his 1st followers were of course all Jews but only 24 years after Jesus (60AD) there was a complete break between the Christian Jews and non Christian Jews. The Christian Jews were cast out, banished, exiled, executed from that time on just about all converts to Christianity came from the pagans and not from among Jews who considered Christians official enemies. In 60AD in Nero's reign Roman court records have Jews attacking the few 'Christians' in Rome at the time, which the Romans could not understand thinking Christians to be Jews too.