Is there any way to obtain Bleeding critical way earlier rather than obtaining +11 base attack bonus due to levels (which makes it minimum level 11) and spending a character level obtained regular feat for it?
To answer your question, you can google: site:d20pfsrd.com/classes/ "Bleeding Critical"
Rangers who are faithful of Zon-Kuthon get bleeding critical as a combat style feat at level 10. Your character would have to be a follower of a sadistic, lawful evil god.
NOTE: at the time of writing, d20pfsrd is undergoing a migration. Your mileage may vary. I was able to use it to identify a class that could get it as a bonus feat, but I had to go to Archives of Nethys to get actual rules.
Boar or Shark Shaman, can pick Bleeding Critical as a bonus feat starting at 9th level, but both must still meet the requeriments. A Faithful Ranger who follows Zon-Kuthon, however, can pick the feat at 10th level ignoring the requeriments.
Faithful (Zon-Kuthon) Ranger
If the ranger selects faithful (zon-kuthon), he can choose from the following list whenever he gains a combat style feat: Agile Maneuvers, Disruptive, Exotic Weapon Proficiency (spiked chain), and Weapon Finesse. At 6th level, he adds Bloody Assault and Improved Trip to the list. At 10th level, he adds Bleeding Critical and Pin Down to the list.