The entire bartending staff is seeking more hours... So honestly the only way I would approve a shift for her would be if she was the only only one trying to pick it up. Which could happen, but with the way the group is fighting for shift probably won't be anytime soon or at least not with a "good" shift. If that is the case, then tell her that -- as clearly and bluntly as you put it above. Then she can decide if it's worth continuing to bang her head against the brick wall of the roster or seek more hours at another workplace.
Totally agree. If there really is such a small possibility for her to pick up extra shifts, I think there is an obvious misunderstanding going on that management is partially responsible for. It sounds like she was told/encouraged to pick up more shifts when she was hired... but in reality those shifts are not truly available to her. So she needs to know what realistically is available to her in terms of hours as well as the things she needs to improve.
There were atleast 8 shifts out of the 60 that were released that no one tried to pick up, so its not an impossibility. When she turned in her availability she was told that she would only get 2 days but to try to pick up shifts when she could. It seems a little ridiculous to believe that we wouldn't be telling the other 29 bartenders the same thing.
Is there a pattern to the shifts that don't get picked up? E.g. are the least in-demand shifts usually in week X of the month, or on Tuesdays, etc.? If so, I would include some of that information in the email, assuming that following the advice is actually likely to result in her getting more shifts. Right now you say you would schedule her only if no one else asked for the shift. If she does what you ask her to, e.g., if next month she applies for 10 shifts during the less popular shifts you indicate, would you make sure to schedule her for at least one, even if she isn't the only applicant? Or will she absolutely only get shifts that no one else asks for, even if she is willing to apply for all 60?
If applying for more shifts at less popular times will get results, then I'd suggest something like:
"Please bear in mind that you are not being denied shifts, other people are being approved. Multiple people applied for every shift that you applied for, and only one could be approved. We look at skill level as it relates to the shift, potential for over time, and general availability when making the decision to approve a shift. During your meeting with [Bossman] and me you were told that with your limited availability you would only received about 2 shifts a week. You are correct you were encouraged to pick up shifts. However, during the month of September there were over 60 bartender shifts available to pick up including the one that you released. You only attempted to pick up 4, all during the last week of the month, which is a popular time to pick up extra shifts. Earlier in the month, particularly [on Tuesdays, during week X, etc.], there were at least 8 available shifts that no one applied for. You will be more likely to get an extra shift by applying for more of them and by trying to pick up shifts during less popular times, such as [Tuesdays, during week X, etc.]. Gaining experience and demonstrating good performance during less popular shifts will also increase your chance of being approved for the more popular shifts."
If there are other limitations on shifts, you might want to mention them so she gets a realistic picture. E.g. "As someone hired for only 2 shifts per week, you're unlikely to receive more than 4 extra shifts per month."