Liquid throughput hall sensor giving odd number of pulses plus only works in horizontal level
I guess it's not an electronic problem. The sensor contains a small impeller which is set into rotation by the liquid. If there is air inside the system, the impeller may not start rotating as intended, or not at all. 

Also, if the flow stops abruptly (as it does when you use a syringe), the impeller may still rotate for a while, resulting in a too high measured volume. This effect of course is amplified when there's air in the system.

I'm not sure if this sensor is the right thing for your project. May be, a scale below the bucket is better? A household scale is available at pearl for 10€. I'm sure you can still replace the internal electronics by your own, just leaving the sensor and mechanical support.

(greetings from Germany)