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Yes, it is possible. I work for the first online data science bootcamp (www.k2datascience.com).
We tell students to cancel all social events and avoid any vacations or trips. You go to work and you study data science. That is the sacrifice that is necessary to maintain your income and successfully transition careers.
As our courses meet 50 hours a week from 8am-6pm, and recommended time spent out of class studying on your own is 10+ hours, I strongly recommend not working 40 hours a week as well.
We do have living expense loans available through our lenders though to cover bills, food, etc and offer free housing for students who live more than 50 miles from campus making it very possible to quit your job so you can focus on the program.
Additionally our students are finding employment within 30 days of finishing their courses on average, often time sooner.
Bootcamps in their very nature are supposed to be intense. They are designed to get you up to speed on key concepts of Computer Science, and the amount of knowledge and experiences you are supposed to take on should take up the majority of your time. There may be programs out there that are designed for students that plan to maintain a full-time job, but I believe it would cease to be considered a 'bootcamp.' I attended a school in San Francisco, Holberton, that is two-years long as opposed to just a few months. It is still recommended that students dedicate 100% of their time to the school for the first nine months, but I do know that some students have attempted to hold down part-time jobs. It has been difficult for most students, but every once in a great while you will come across a student that can handle both at the same time.
Coding Bootcamps start at 9 o'clock in the morning and finish at 6 o'clock in the evening. So ... you can't be at two places at the same time. Unless you work the other hours of the 24-hour clock.
However, you can still continue your work and take online coding courses like the one at https://www.techcareerbooster.com/online. They require, at least, 15 hours per week, which is very doable. They are designed for those particular students that they want to work at the same time. They assign to you a mentor which follows you throughout the whole journey of your studies. And there is a big difference to bootcamp: You don't have to pay the whole amount in advance. You pay as you go and you take only the parts of the course that you want. Nevertheless, they do have the exams and they give you a certificate of completion.
You can sign up, since they do not ask money for that. You will see their curriculum and you can decide.