Jesse, I don't build many board bows but if the runoffs are not too drastic you can add a simple backing of brown grocery bag paper, linen or silk cloth. Any of these are easy to do with carpenters glue(TiteBond or Elmer's). A backing is good insurance to help prevent breakage. If the run offs are too drastic these backing materials won't keep the bow from breaking.
Check out George Tsoukalas' website. It has all the info you need to build a board bow from selecting the correct board through the tillering process and the finish work at the end.
Keep us posted on your progress and ask all the questions you may have. Posting pics of your progress or problems helps us help you.
Good luck on your first bow. Be patient and don't get in a rush. If you can't concentrate on your work, put it down and come back when you really feel like building a bow. We have all been through what you are experiencing now. Most of all, HAVE FUN! That's what it is all about!!!