Deficits in bimanual coordination of older adults have been demonstrated to significantly limit their functioning in daily life. As a bimanual sensorimotor task, instrument playing has great potential for motor and cognitive training in advanced age. While the process of matching a person’s repetitive movements to auditory rhythmic cueing during instrument playing was documented to involve motor and attentional control, investigation into whether the level of cognitive functioning influences the ability to rhythmically coordinate movement to an external beat in older populations is relatively limited. Therefore, the current study aimed to examine how timing accuracy during bimanual instrument playing with rhythmic cueing differed depending on the degree of participants’ cognitive aging. Twenty one young adults, 20 healthy older adults, and 17 older adults with mild dementia participated in this study. Each participant tapped an electronic drum in time to the rhythmic cueing provided using both hands simultaneously and in alternation. During bimanual instrument playing with rhythmic cueing, mean and variability of synchronization errors were measured and compared across the groups and the tempo of cueing during each type of tapping task. Correlations of such timing parameters with cognitive measures were also analyzed. The results showed that the group factor resulted in significant differences in the synchronization errors-related parameters. During bimanual tapping tasks, cognitive decline resulted in differences in synchronization errors between younger adults and older adults with mild dimentia. Also, in terms of variability of synchronization errors, younger adults showed significant differences in maintaining timing performance from older adults with and without mild dementia, which may be attributed to decreased processing time for bimanual coordination due to aging. Significant correlations were observed between variability of synchronization errors and performance of cognitive tasks involving executive control and cognitive flexibility when asked for bimanual coordination in response to external timing cues at adjusted tempi. Also, significant correlations with cognitive measures were more prevalent in variability of synchronization errors during alternative tapping compared to simultaneous tapping. The current study supports that bimanual tapping may be predictive of cognitive processing of older adults. Also, tempo and type of movement required for instrument playing both involve cognitive and motor loads at different levels, and such variables could be important factors for determining the complexity of the task and the involved task requirements for interventions using instrument playing.