@Craig74 It's not only not normal, but the host is violating AirBnB's terms of service by conducting a financial transaction outside of the AirBnB platform. You should not play along, as it could lead to further problems.
If I were you, I'd send her an AirBnB message telling her that you cannot put up a security deposit other than one within AirBnB. The reason to write her within the AirBnB message system is that if she repsonds there in any detail, AirBnB will be able to see what she's said. (You should never have corresponded with her via email.) As soon as she dos make a definitive response, contact AirBnB to cancel the reservation w/o penalty for you. (By no penalty, I mean that they shouldn't charge you their service fee.)
Even if the host refuses to correspond within AirBnB, send her at least one more similar message. Her lack of response will bolster your case when you contact AirBnB.
Worst case, go ahead and cancel on your own. You'll be charged the service fee, of course. Hopefully, your cancellation will be far enough in advance that you don't get charged a partial fee for the booking.
Good luck!