There is good bacteria in your anaerobic, or cold composting method. The cold compost can be used in making compost tea, since the water will be oxidized with bubbles, only the aerobic bacteria proliferate. I wouldn't use a pump in your cold compost. You are making a lot of really good bacteria, enzymes, fulvic acid and humic acid which are great for the soil. Stirring it really well will help it cook faster.