First of all, in this sense WILL and MUST are pretty much equivalent. The latter is stronger and in more frequent use. (Of course, WILL is also often used to form the future tense, but that is not how it is used here.)
Next, it's worth distinguishing between WILL BE and WILL HAVE BEEN. Let's look at the sequence of events:
- She was fined.
- She started asking herself whether cameras are a good idea.
In this case, it would be correct to say, "She WILL [or must] BE asking herself whether...." Here, WILL is a speculation about the present, equivalent to "She is probably asking herself...."
However, if you consider the sequence of events to be three rather than two:
- She was fined.
- She started asking herself whether cameras are a good idea.
- The newspaper article was written.
then "She WILL HAVE BEEN asking herself whether..." is the right way, because it is a speculation about the the past (i.e. before the article was written), equivalent to "She has probably been asking herself...."