Yes, you should start asking - and there are good ideas here.
Also, you don't have to ask exclusively in the context of death - you can ask so that if, heaven forbid, she became ill for some period of time, you want to be able to keep her cell phone bill paid, make sure she gets critical care, etc...
I'm a fan of the "hey, I heard about this nightmare scenario that happened to a friend and it made me think we should talk about this stuff" setup. Also, depending on your relationship w/ your mother, you can say this kind of planning is really a gift to you - it will eliminate some worry/stress for you - so she's doing you a favor in setting these things up.
Good luck OP, it's tough stuff when they're alive, tough while they're failing, and tough when they're gone. Good for you for trying to get a handle on things where possible.