That is precisely why this method may work well for you. It is not a cover to cover or chapter to chapter reading plan. In fact, you will be devising your own plan. How many chapters do you want to read per day or week? How many times a week will you be putting time aside for Bible reading?
It works well for many people to read one section of the New Testament, a section from the Old Testament, and a section of the poetry books at each reading. So to begin your reading plan, you would be reading as much as you decide to cover from Genesis, Matthew, and perhaps a chapter from Psalms or Proverbs on your first day. Know from the beginning that if you miss a day, it is not a good idea to try to "make it up" the next day. That could possibly tend to turn it into what feels like a chore instead of enjoyable time.
That is just one plan that you may choose. You may enjoy reading one of the stories you remember from your childhood for the start of each reading section, followed by something else you choose. No matter which plan you formulate for yourself, however, be sure to first make a chart listing all the books of the Bible and how many chapters are contained within each book. It takes a bit of time to do this, but it is a great feeling of accomplishment when you can mark off a chapter as being read.
Do you have a time frame in which to finish the entire Bible? Will you be studying as you go along, or simply reading? No matter how long you wish it to take, divide the number of chapters in the Bible by the amount of time you want to take to complete the reading. Remember to add the extra chapters when you are doing the math if you are using a Bible with the added books of the Apocrypha included.
Another thing to keep in mind is to choose a reading time that will most likely present the minimum amount of interruptions. If life gets hectic around dinner time in your home, don't make your reading time 6:00 p.m., for instance. If you get tired and sleepy while reading in bed, don't plan for your Bible reading time to be after you retire in the evening. It should be a time when you probably won't be interrupted and when you can be relaxed and prepared to understand what you are reading.
As mentioned before, be sure to have study aids nearby if you are going to be delving further into the scriptures that you read each day. There are many reference books that will help to explain what the words mean that you have read and thus help the reader to study the scriptures. There are also many study Bibles that have teaching points and articles about the text and notes in the margins.
Consider buying a notebook where you can keep track of scriptures that were especially meaningful to you, or stories that you want to remember. It may even serve as a journal of sorts to write your feelings about what you have read.