Two methods.
One, and my main method, is the Liturgy of the Hours; as many know the main content of the Liturgy of the Hours is scripture. Other than the hymn, patristic/hagiographic reading at the Office of Readings and intercessions of MP and EP, it is virtually all scripture. So I pray the psalms, and read the shorter readings at each hour, as well as the longer reading at the Office of Readings. I generally chant the hours in Latin except for the readings (and the Office of Readings which I recite in my vernacular, French). My method is to chant the psalm in Latin, then silently read through it in French afterwards. This has the effect of the Latin chanting being a sort of mantra that causes a rupture from the world around me, to allow me to better absorb the psalm when I read it.
After the readings, I observe a moment or two of silence to try to absorb the lesson.
My second method is something I’ve neglected for too long, and that’s Lectio Divina. At the moment I’m on an extended sabbatical, so I generally do lectio between Morning Prayer and Terce. I try to devote 30-45 minutes to lectio most days.
For lectio, I generally select the gospel reading for the day from my missal; I will often first read the Epistle/OT readings to set everything in context, and then do Lectio on the Gospel.
I find having a systematic ritual and routine very helpful. The key I think to reading the Bible is to not try and project your interpretation on what you’re reading, but instead try to discern what it is saying. That can lead to surprises. Here is a good paper on Lectio:
benedictine-oblates.org/2013/txt/txt-03-en.pdf