Bedroom circuit breaker is a gfi breaker and is 15 amps. The microwave is on a separate 20 amp breaker. When the microwave is used it continues to work, but the bedroom breaker is tripped. What should I do?

Is it a GFCI or an AFCI that trips, they are very different.

This symptom is very unusual and is out of a DIY capabilities. For an appliance to be on a separate 20 amp CB and a 15 amp CB for the bedroom to trip, something weird is the cause. Your best to get a good service electrician to troubleshoot the situation.

Perhaps two circuits are sharing a neutral... not such a good idea if that is the case. At any rate please follow tkrussell's advice ASAP.