> [...] and having to take it with her to the bathroom (feeling somewhat self conscious about how her more frequent trips appeared to her younger, generally male coworkers)
Get one of these kitchen timers [1].
Set it to about 25 minutes.
When it goes off get up from your desk and spend a few minutes walking around the office.
Return to your desk, reset the timer, and go to prior step.
When you wish to visit the bathroom do so on one of your strolls around the office.
Coworkers will ask what you are doing (this is one of the reasons to use a physical timer instead of something running on your computer...it will be noticeable). Here are three reasonable explanations for why you go on a stroll around the office every 25 minutes or so.
1. It is unhealthy to sit for extended periods. If you get up and move around every 25 or 30 minutes or so most of the bad effects of sitting can be eliminated or greatly reduced [2].
2. When solving problems it is best to have a mix of "focused mode" and "diffuse mode" thinking. Get into focused mode and then when the timer goes off you can take a break and let diffuse mode take over. That walk around the office is perfect for some diffuse mode thinking. There is much more about this in the "Learning How To Learn" course available at Coursera.
3. There is a time management technique called the Pomodoro Technique [3] built around breaking tasks into 25 minute chunks paced using a timer.
Once people see you doing this I'd not be surprised if several other coworkers start doing the same. Reason #1 alone will get a lot of people.
Once several people are doing this no one will have any idea how often you visit the bathroom (well, except for those people whose can see the bathroom from their desks). And as a side effect you'll have better health and productivity.
[1] https://www.amazon.com/60-Minute-Kitcher-Timer-Tomato/dp/B00...
[2] http://ergo.human.cornell.edu/cuesitstand.html
[3] https://en.wikipedia.org/wiki/Pomodoro_Technique