Consider schools that that offer dual degree programs. Many business schools have dual degree options which allow students to earn both an MBA and a master's simultaneously. Some schools even offer classes that will count toward both degrees, allowing you to complete both degrees faster than if you enrolled in each program separately.
Choose a subject for your master's degree in which you already have a strong background. Not only will you need to apply for admission directly to an MBA program, but you will also need to submit an application to the department where you will earn your master's degree. You will find the process of enrolling in both programs to be more straightforward if you have already taken the prerequisite courses needed for the master's degree.
Consider schools that offer internship programs targeted to dual degree students, which will allow you to gain business experience in a field related to your master's. You may even be able to receive course credit for both degrees by combining an internship with academic work.
Don't automatically rule out a field for your master's degree because it does not seem to directly relate to business. An MBA degree can be broadly applied across a range of fields such as healthcare, engineering, international relations, information technology, education, communication or the arts.
Investigate part-time MBA programs that you can complete while also enrolled in a full-time master's program. Many MBA programs offer evening and weekend courses to accommodate students with busy schedules. This option could allow you to finish both degrees in a shorter period of time without overwhelming yourself with two full-time course loads.