This paper proposes a wireless sensor device for the real-time acquisition of bioelectrical signals such as electromyography (EMG) and electrocardiography (ECG), coupled with an inertial sensor, to provide a comprehensive stream of data suitable for human activity detection, motion analysis, and technology-assisted nursing of persons with physical or cognitive impairments. The sensor is able to acquire up to three independent bioelectrical channels (six electrodes), each with 24 bits of resolution and a sampling rate up to 3.2 kHz, and has a 6-DoF inertial platform measuring linear acceleration and angular velocity. The bluetooth low-energy wireless link was chosen because it allows easy interfacing with many consumer electronics devices, such as smartphones or tablets, that can work as data aggregators, but also imposes data rate restrictions. These restrictions are investigated in this paper as well, together with the strategy we adopted to maximize the available bandwidth and reliability of the transmission within the limits imposed by the protocol.