Yes, there was both criticism and ridicule.

To take two examples, Celsus of Origin wrote a polemical attack on Christianity, The True Word, unfortunately only fragments of it survive as found in Origen's reply work, Against Celsus. Nonetheless, Celsus considered the idea of the incarnation to be incompatible with notions of God, the resurrection as contrary to rationality and the natural order, and Jesus as a low-pay-grade magician. Celsus' work is typically dated to the 170s. You can read a translation of the fragments here.

Porphyry wrote a 15 volume work, Against the Christians, which unfortunately also only survives in quotations among his opponents. He wrote in the late 3rd century. Included in his attacks is a critique of reliance upon the book of Daniel, which Porphyry said was dated to the 2nd century BCE, and so was historical, not prophetic, in its 'predictions'. Translations of some of Porphyry are found here.

Lucian of Samosata wrote a satirical work making fun of Christians and especially their gullibility, in his Passing of Peregrinus, in approx 165-175.Translation available here. Lucian's work shows accurate knowledge of Christians at the same time that it makes fun of them.

However the types of criticism/ridicule levelled at the Bible are not always the types of ridicule common today. Hebrew-centric was not largely a critique, the types of incredulity were not those that come from 21st century naturalistic rationalism, etc..