I hesitate to stamp Bible-reading as an obligation. We resist things that oblige us to do something, whether it's brushing our teeth or paying taxes. So let me speak not only as a catechist but also as a 30-year Bible-reading Catholic: Don't do it because you have to. Do it because it's the most wonderful choice you can make for your life!
This will come as a relief to new Bible readers: If you attend Mass regularly, you're more familiar with the Bible than you imagine. The lectionary—the book of readings used at Mass—covers a cross section of passages from the Old and New Testaments. So even though the stereotype claims that Protestants know their Bibles and Catholics don't, active Catholics may have a more comprehensive appreciation of scripture than some fellow Christians, who tend to focus on specific sections according to their denomination's (or pastor's) inclinations.
As far as personal reading goes, the idea of opening to Genesis, page one, is probably what makes many people shrink from the idea. You don't have to read scripture cover-to-cover (though kamikaze readers like me may enjoy the challenge). Some folks will appreciate support for the journey: Many parishes now sponsor Bible study or faith-sharing groups precisely for that reason. If private meditation works better for you, consider subscribing to a scripture journal that offers a daily guide through selected material.
You may also want to take baby steps in: There are page-a-day books geared to the five-minute reflection approach that provide a great introduction for beginners. It's like taking a swim class: Sign up at the level that suits your present skill and go from there. No one expects you to dive in at the deep end!
The Bible is the Mt. Everest of books; you won't conquer it at once, and it will take training to reach the exotic parts, like Maccabees or the Book of Revelation. But within a year you'll be surprised how much more comfortable and fit for the journey you are. Start today. "One does not live by bread alone, but by every word that comes from the mouth of God" (Matthew 4:4).
Lectionary based: "Exploring the Sunday Readings" (Twenty-Third Publications)
Examines one book per issue: God's Word Today journal (Twenty-Third Publications)
Explorations by themes: Threshold Bible Study
A page-a-day, geared to the current year: A Book of Grace-Filled Days (Loyola Press)
CatholicsRead program: Bible study and resources from the Catholic Book Publishers Association, www.catholicsread.org/.
God's Word Is Alive by Alice Camille (Chicago, ACTA Publications, 2007)