As you already know, Israel was commanded to abstain from eating blood (Genesis 9:4). What was the process of draining the blood in ancient Israel? I know a modern process involves heavily salting the meat to extract all of the blood, but the only process I could find in the Torah was to "pour it on the ground as water" (Deuteronomy 12:16; 15:23). It seems as if the ancient Israelites were able to kill and prepare an animal relatively quickly so the process must not have been that long or complex.
Even today, instead of heavy salting, waiting and washing, meat can alternatively be quickly roasted or grilled and the blood drips out, but there are special laws regarding the spit, grill and/or pan which absorb the blood. You are correct that this process is much quicker and was probably more common in Biblical times, but in today's modern kitchens, it's easier just to buy the meat already salted and ready for cooking.