I suspect your grandmother was just as busy as you were when she was your age - and perhaps more so, since she probably didn't have all the labor-saving devices you have.
And yet she still found time to read her Bible every day. How did she do it? I don't know how she'd answer that question (although you might ask her), but I suspect the reason is because she believed it was important. She gave it priority - not out of habit, but because she knows that the Bible is God's Word, and we need to hear what He has to say to us through it.
Think of it this way: How many meals do you forget to eat in a week? Probably none - because you know it's important to eat, and it gives you pleasure. But which is more important: your body or your soul? Don't starve yourself spiritually, but set aside time to be alone with God every day - reading His Word, meditating on its truth, and praying. Job said, "I have treasured the words of his mouth more than my daily bread" (Job 23:12).
Begin by examining your own relationship with God. Is Christ real to you, and do you know that He lives in your heart? If not, turn to Him in repentance and faith, and commit your life to Him. God loves you, and Christ died and rose again for you. Your life will never be the same once you know Christ. Open your heart to Him, and then learn to walk with Him every day.