Have you done any work for her up to this point? If so charge her for that.
As for charging a fee for not using you, you can try it but don't expect her to agree (or to come back to you in future). Clients have a choice of who they pay to create work for them, and if that's not you it's best to just take it on the chin and move on.
If you want to back-engineer a CMS into an existing website then that's going to be a fair bit of work?
Or have you done the initial design and it now needs to be converted into HTML/CSS etc. If that's the case, then she will not be able to do this herself, it requires a web designer to convert a design into a CMS website.