I agree that keeping up with the daily Mass Readings is a great way to read a little bit of the Bible every day. So is praying the Liturgy of the Hours, the Divine Office.
Just keep in mind that neither one of those privileged vehicles, however long pursued, will present to you the entirety of Sacred Scripture. They are simply collections of pericopiae, that is, selected episodes and passages cut-and-pasted, as it were. A two-year cycle for weekday Masses, and a three-year cycle for Sunday Masses, and a 4-week cycle for the Hours necessarily leave out a lot of the Bible.