My question is - how does online acess help if I don't have an account at a bank in my bugout location?
It depends on how robust the online access is. For example, if it has a bill pay system (which I suspect most do) you could go online and "pay yourself" or a friend at your new location and then cash the check. You can also make sure that your bills (like insurance premiums and cell phone company ;-) are paid via the online bill pay system. Of course, this is for more long-term situations, and you could probably do as much with a checkbook. If your online access allows transfers to other banks, you could transfer money to a the account of a friend who banks at your remote location.
Online access varies from bank to bank. I have an account at BofA that has really robust online capabilities. I also have an account at a different local bank that has pretty lousy online capabilities (so bad that I actually prefer writing a check to using those online capabilities).
-Kuovonne