First of all Judaism spread quite a bit before Christianity, in the first century there were about 5 million Jews spread out in the entire Roman Empire. While at the same time the Roman Empire itself had a population of about 50 million, in other words it was 10% Jewish^1,2 .

Judaism actually attracted quite a number of "God-fearers" or those who were attracted to the Jewish religion, joined in services but for whatever reason did not become inducted into the faith. This is because the Jewish faith deterred conversion; converts had to follow strict Jewish laws, had to be circumcised, couldn't serve on the Sanhedrin and women converts couldn't marry priestly families.^3

Also its a bit silly to me to say that the Jews didn't spread their religion during this period as just a hundred years prior to the common era John Hyrcanus forcibly converted the Idumaeans.

One can say that Judaism did spread more, out of its variant form of early Christianity. It's no secret that the major Christian centers were also major Jewish centers and that proselytization of Christianity was focused on Jews not Gentiles. It would grow even larger when the Apostle Paul and the Council of Jerusalem would make the "God-fearers" full members of their churches rather than half-Jews in the synagogues.

Furthermore, even with Christianity's spread it isn't as if Jews ceased proselytizing either. Conversion to Judaism was a common phenomenon in the Greek portion of the Empire up until the tenth Century. We know this because there were decrees every twenty years forbidding the practice. "The further away from Palestine a country was situated, the less pure racially and ethnically its Jewish settlers were."^4

I would say the reason Judaism didn't spread more is because they were competing against Christianity and lost. If it weren't for Christianity's implicit respect for the Jewish religion it would probably have ceased to exist or only as a minority racial faith like Yazidism or Zoroastrianism. Christianity was just far too attractive out of all the Imperial cults for the political elite, and its lenient behavior towards converts helped it appeal to the common folk.

^1 Stark, The Rise of Christianity

^2 Frier, Demography

^3 O'Grady, And Man Created God

^4 Kriwaczek, Yiddish Civilization