The most risk free and effective taming method is to
1. Build a taming pen
2. Lure or drop him in
3. Build a bed and storage chest next to it
4. Tranq the bear until he starts to show blood
5. Put your inventory in chest
6. Let the bear kill and eat you.
8. Respawn in bed, get inventory and finish tranqing. No need to switch to a bow or use traps.
This is very effective because the bear will regenerate a lot of health from eating you. And you will have no risk knocking it out. If you do this correct, maybe even kill yourself twice, you can get the bear to be at 80-100% health when you knock it out. Thus increasing chances of it surviving it someone/something hits it.
To reduce chance of killing it while trying to knock it out is by shooting with a primitive crossbow without delay until it starts to show blood then switch to a regular bow and then space shots 7 seconds apart - works every time for me no matter the level