Respiration rate is considered as a critical vital sign, and daily monitoring of respiration rate could provide helpful information about any acute condition in the human body. While researchers have been exploring mobile devices for respiration rate monitoring, passive and continuous monitoring is still not feasible due to many usability challenges (e.g., active participation) in existing approaches. This paper presents an end-to-end system called RRMonitor that leverages the movement sensors from commodity earbuds to continuously monitor the respiration rate in near real-time. While developing the systems, we extensively explored some key parameters, algorithms, and approaches from existing literature that are better suited for continuous and passive respiration rate monitoring. RRMonitor can passively track the respiration rate with a mean absolute error as low as 1.64 cycles per minute without requiring active participation from the user.