Good news! Verses actually supports 100% offline functionality already! Just make sure you've already created your account and downloaded your preferred translation (if you want another besides KJV) and then you'll be good to go! The phone will save all your progress offline as you work and then the next time you have an internet connection it will sync to backup/save your progress (e.g. in case you want to switch to a different phone in the future).
Drop us a note at firstname.lastname@example.org if you have any questions!