Ok I tested this on 20 runs, in the upper depths there are 15 rats close to first bonfire the total run for me took approximately 2.5 to 3 minutes, I was level 48, and had gold serpent ring, with 10 available humanity, my item discovery was 410, I was also human. The purpose of my exercise was to fill my inventory and bottomless box for a total of 198 humanities, then if you get humanity from bosses, you could have a total of 297 humanities not to mention any twins.
Ok, I preffered soul arrow and great soul arrow (for the three giant ones), dont forget the one on the right and the 2 in the boxes left to the giant ones. for any melee chars I suggest a sweeping scythe to take them out quicker. also forget about the slimes you dont need to farm them for titanite, its a rare drop from them even at 410 item disc, go to blight town and do leeches for titanite.
I will do the math based on my tactics. In 20 runs I averaged 2.9 humanities each time. Assuming you do not have any humanity in your inv or box your goal is to get 198 total. 99 for inventory and 99 for box. so 198 divided by 2.9 is 68, this is the amount of runs you will need to make. at an average clear time bonfire to bonfire 3 minutes this will take 3.4 hours, then you can get summoned for quelaag, sif, or iron golem fights to get the remaining 99 in your hud. I know farming is tedious but for a mid range player, 3.4 hous is nothing compared to the reward of having that much stored humanity.