After finishing my bachelor's degree, is it manageable to continue onto a master's program while on active duty?

As with our Bachelor's, not all Master's programs are created equal. It is entirely possible to do a Master's while AD. But you will need to check out the program requirements for timelines, research, projects, etc. If your prospective Master's program is going to require a thesis based on 6 months of original research, that is going to be VERY hard to accomplish. If it requires a 50 page meta-analysis of existing research, that is probably doable.

Master's classes, in my experiencence, are little different from Bachelor's classes, at least regarding timelines. Each class takes more work, but you take less of them. If you take it slow and steady, in a program that is flexible and works with you, you should be able to complete a Master's in 4 years, while still doing full time Soldier stuff. That would be one course each trimester. Which is entirely doable.

Of course, the expectations for the coursework are higher (longer papers, more research, and higher standards)... But I assume that is not what you were asking.

I think in general yes it is possible. I recently started a MS and I have a full time job that requires me to work four 12 hour shifts and I'm in the NG in a position that requires more than the advertised "one weekend a month." It's a lot but manageable. My program has one class at a time for eight weeks. Which is still full time but I don't have to juggle multiple professors competing requirements.

Of course it is. I have many friends who actually completed PHD’s. Where there is a will…

That really depends on you. It is dependent on you and your work load. I have seen some folks have an MOS and duty station that was flexible enough to support knocking out degrees. But I have also seen work loads and duty stations where the service member struggled to finish an Associate's due to work and family commitments.

Degrees are generally a good thing. When you transition to civilian life, they become "door openers." They may help you get the interview but getting and keeping the job depends on more than a degree. This is a good time to look at your life goals and see if a master's degree is what you need to meet those goals.

Two considerations: will an advanced degree help your Army career and will an advanced degree help you get the job you would like when you enter civilian life. If you're planning on staying for 20 or more, then decide if a Master's Degree will help you make the next two promotions. If it isn't very important, then decide what else Might help more. If it is very important, then go for it. As for employment on the outside, few jobs require an advanced degree and many of those require specific types of advanced degree. For example a Master's of Social Work may be required to be a licensed Social Worker in some states. A Masters Of Medical Administration may be necessary to find work as a hospital administrator. You should start looking at education requirements in the career fields in which you might want to work after the Army. Check job requirements in USAJobs for Government jobs in your chosen field. Look at Department of Labor information. In some cases, a Master's Degree is a stepping stone to a PhD. If you want to earn a Doctor's Degree so you can teach at the college level or do research, then get your Master's Degree in the same or closely related area as you want to get your PhD.