It's easy enough to do the math to find the lowest level possible. I guarantee it's been done at the lowest possible level.
this caught my interest. so i did some work to see what the absolute lowest possible level for that job would be and if my math is correct, it would be 19. gray slouch hat and gray work shoes, with the golden necklace and a mustang combo along with a black shirt. since you cant wear any of the cotton jackets before lvl 20. But you must have also completed the first three quests of the introduction series, the first of the cattle herd, and up to "the last ingredient" on fire heart for a total of 8 skill points. which you can then switch over to setting traps after you complete the lvl 14 grandfathers quest. Now all of that would put a level 19 pure trapper at a totally lame 279 points towards hunting bears, a job that requires 280. to get those last few points that you need, you would have to be a dueler or a soldier. Complete the quests "Sweet work" and "Wisdom" respectively. which is easily done, and get the 1 skill point in shooting as a reward (+2 skill points for soldier) and switch it over to setting traps. that would would be 279 + 2 = a cool 281 as a dueler. and 283 as a soldier.
A level 19 pure trapping dueler or soldier with a gray slouch hat, gray work shoes, golden indian necklace, mustang, and a black shirt that has switched over every possible skill point over to setting traps, is the lowest leveled player that can hunt bears.