According to Catholicism, what does the Bible teach about sins of omission? According to Catholicism, what does the Bible teach about sins of omission?
According to Summa Theologiae, II-II, q. 72, a. 6 by St. Thomas Aquinas:


  On the contrary, Omission and commission are found in the same species of sin. For the covetous man both takes what belongs to others, which is a sin of commission; and gives not of his own to whom he should give, which is a sin of omission. Therefore omission and commission do not differ specifically.


Read full 'Whether sins of commission and omission differ specifically?' article here: STh, II-II, q. 72 on newadvent.org

Accordint to Catechism of the Catholic Church, §1853:


  Sins can be distinguished according to their objects, as can every human act; or according to the virtues they oppose, by excess or defect; or according to the commandments they violate. They can also be classed according to whether they concern God, neighbor, or oneself; they can be divided into spiritual and carnal sins, or again as sins in thought, word, deed, or omission. the root of sin is in the heart of man, in his free will, according to the teaching of the Lord: "For out of the heart come evil thoughts, murder, adultery, fornication, theft, false witness, slander. These are what defile a man." (Mt 15, 19-20) But in the heart also resides charity, the source of the good and pure works, which sin wounds.


CCC, The Different Kinds of Sins on vatican.va
(This is the only paragraph indexed under 'omission' in CCC)

Certainly, there is more on this topic in other documents of the Catholic Church and writings of Church Fathers and Doctors.