How to connect a 2.4ghz 4ch RC receiver to a brushed dc motor controller?
RC servo signal is a 1-2ms pulse with repetition period of ~20ms. Ebike controllers generally accept an analog voltage between 0-5V (with 1V=off and 4V = full throttle). You will need an interface to convert from one to the other. Possible solutions range from purely mechanical (servo attached to a potentiometer) to an MCU with D/A converter. 

The Arduino can measure servo pulse width with pulseIn() and produce an 'analog' output with analogWrite(). On most Arduinos the analog outputs are actually 0-100% PWM at ~490Hz. To convert this to true analog you need a low pass filter or integrator which averages the pulses, eg. this simple RC filter:-







simulate this circuit &ndash; Schematic created using CircuitLab

A side effect of integrating the PWM pulses is slower throttle response. Here is the result of simulating the above circuit in LTspice, with a 0.5 second 50% throttle burst:-