I've always taken the 'bits and pieces' clients as par for the course - as a service provider it's my job to make working with me as easy as possible which sometimes means weeding through fifteen emails that all contradict eachother

. And, the time it takes to translate their project is as billable as any other hour, so it's not something I begrudge them.
BUT - if a client wants two hours and spends half that time emailing impossible to decpher requests I think it's a great idea to help set up systems to keep her time with you optimized. She'll likely appreciate the help!

I think even just telling her straight up front that you want to address this - and frame it from her perspective, in terms of saving money and fully utilizing the time she's buying - she may have some input as to how you can help her get organized (and there's your first billable week with her right there

)