Bleed is usable in PvE as a primary damage source, and scales well into higher NG+ cycles due to the hp% based damage, but for maximum DPS is generally better as a tertiary source of damage. I've done extensive testing offline replaying bosses over and over, and a Hollow Barbed Straight Sword with Carthus Rouge will kill an NG boss 40-70ish % faster than a Bleed Infused Bandit's Knife with 51 Luck +5 from a Hollow Offhand. (By the way the softcap for Bleed Infusions is actually 56 luck, not 50. You get 2-3 extra bleed aux from 50 to 56, as opposed to the 10+ levels past 56 without a single additional bleed point.)
Bleed can be seen logically as simply extra damage every x number of hits, with the x being decided by the weapon's bleed buildup. The issue is breakpoints and the increasing amounts of bleed necessary to reach fewer hits. For example, through my testing I've found that Champion Gundyr has anywhere from 250 to 290 Bleed Resistance (likely 250 logically) A Blood Infused Bandit's Knife has a bleed buildup of 76, bleeding Gundyr in 4 hits. Bleed buildup does 'overflow' however, meaning that the additional bleed buildup in the hit he was bled is simply added to the next buildup counter, meaning the next bleed will only take 3 hits (7x76= 532). A Hollow Barbed Straight Sword with Carthus Rouge has a bleed buildup of 56, meaning only 5 hits to bleed, and then 4 hits to bleed on the next cycle, which is consistent with my testing. So what's the catch, Bandit's Knife obviously bleeds in 1 fewer hit, meaning ~30% faster bleeds? At 30/30/51(56) (Strength/Dex/Luck) a Blood infused Bandit's Knife deals 185 damage. At the same soul level, a 40/40/40 Hollow Barbed Straight Sword deals *431* damage.
Assuming a 5000 hp Champion Gundyr target, Blood Infused Bandit's Knife bleeds will deal 950 damage (5k*.15+200). Over the course of a 14 hit sample (enough for each weapon to finish one complete bleed cycle)with 4 bleeds, the target will be bled for 3800 damage, with an additional 1850 damage from the hits themselves for a total of 5,650 damage. This is perfect world and not accurate considering enemy resistances to the hit damage.
On the other hand, a Hollow Barbed Straight Sword will bleed for an average of 825 damage (5k*.15+75) (Carthus Rouge adds 100 bleed damage if it procs bleed, whereas an innate bleed weapon only adds 50 if *it* proces the bleed, I simply averaged the two). Over a 10 hit sample with 3 Bleeds, it will deal 2475 bleed damage, with an additional 6034 damage from hits, for a total of 8,509 damage over 14 hits.
5,650 vs 8,509
Just aboute exactly 50% more damage is dealt by the Hollow Barbed Straight Sword over the same sample of hits. The Bandit's Knife does attack faster and uses less stamina, but I tested for that as well. In raw TTK, it took me 14 seconds to kill with a Bandit's Knife with 30/30/51(56), and 9 seconds to kill with the Hollow Barbed Straight Sword, so about another 50% faster result.
Now you may ask, but what about NG+7, where the HP% is more important? 8652 damage over 14 hits with Bandit's Knife, 10,205 with Hollow Barbed Straight Sword. Closer, but still no cigar for the Bandit's Knife.
Tl;dr Hollow weapons, especially high damage swords like Carthus Curved Sword and Barbed Straight Sword with Carthus Rouge will solidly outdamage blood infusions in 90% of cases.