I regularly advocate that people read the Bible s-l-o-w-l-y, prayerfully. I encourage the practice of Lectio Divina where I suggest “Use only a small passage of scripture. This is not drinking beer it is sipping a liqueur.” I have been creating a series going through Matthew’s Gospel line by line, word by word (start here).
But, I also regularly advocate that people read a whole book of the Bible at one sitting. Depending on your reading speed, it takes about, say, an hour to read Mark’s Gospel. Some of the New Testament letters were surely written with the intention that they be read aloud in one sitting.
Some people memorise large portions of the Bible. Rev. Bert Marshall, for example, has been telling the whole Gospel of Mark in performance from memory for a dozen years now.
Bishop Kelvin Wright has been writing about reading the Bible, basically a book in one sitting, and from a version without the later additions (chapters, verses, headings, interpretive footnotes…):
For years, I now realise, I have studied the New Testament, but not actually read it. Every time I’ve sat down with those familiar passages, as I have done pretty much every day for decades, it has been with a text divided up into chapters and verses by Erasmus 1500 or so years after they were written. Every version of the Bible I own, except one, has copious footnotes and cross references to which I turn when befuddled. So now, I am reading it, not studying it, in the exception, my one version from which all that stuff has been deleted. It’s just me and these old words. I’m reading each of the documents of the New Testament in one sitting, and leaving a few days between each one to give a bit of thinking space. … Reading them, as we usually do, piecemeal, in small shards wrapped liberally in interpretation, means that all sense of the flow of the text is lost, and we become engaged in an odd exegetical spiral. …
Each of the Gospels tells a story of Jesus, and I had never quite noticed before the extent of the differences between them. There is Mark, for whom Jesus bursts into history and for whom everything happens suddenly: “and straightway” is his very favourite phrase. There is Luke with his meandering interest in story and whose definitive account of the resurrection does not happen at the tomb but on the road To Emmaus. There is Matthew taking pains to weave his account of Jesus into the Old Testament narrative. There is John with his lengthy monologues, placed into the mouth of the writer and of Jesus. I read each of these, and the person of Jesus of Nazareth has never seemed more clear. Or more enigmatically hidden….
The version Kelvin is using is Bibliotheca. This is a reworking of The American Standard Version (I was in from the Kickstarter beginnings). This “American Literary Version” changes archaic forms (“firmament” to “vault”; changes “thou”, “doth”; replaces LORD with YHWH; and fixes ASV errors and mistranslations).
There are other translations trying to encourage reading longer texts. The Kingdom New Testament, a translation by N.T. Wright, reads more easily than some. He has this in mind. He writes,
It’s good to read right through chapters, sections, and entire books at a single sitting. The “books” which make up the New Testament weren’t written to be read in ten-verse sections at a time; imagine what would happen if you tried to listen to a symphony that way, or to read a novel at the rate of a single page once a week. I hope this present translation will make it easier for people to do this, to feel the flow and pull, the energy and power, of large chunks at a time. (Preface xiv).
I wouldn’t go as far as N.T. Wright’s claim that all the New Testament “books” weren’t written to be read in sections at a time. The synagogue tradition of reading portions of the scriptures was already well established, and Jesus is presented as following this tradition. Most scholars, in fact, would hold that the Gospel stories were communicated in well-polished stories (pericopes). There are scholars who would even see some pericopes as standing in relation to readings from the Hebrew scriptures. So it is not too difficult to imagine a meeting of First Century Christians reading sections from the Hebrew scriptures and following this with a well-known, at-that-stage-not-yet-written-down story from the life of Jesus.
I do encourage you to a both-and approach: read large swathes of the scriptures at one sitting and practice slow reading of very small sections.