Load up the northwest map and select the black dog area. Set the time to 9:00 or 10:00. Make sure you have the 30-06 equipped. There should be a bear right in front of you. If not press pause and select restart hunt.
The 30-06 is not a big enough gun to penetrate the hide of a grizzly so it will probably take several shots to kill it. If you dont get lucky and get a vital shot with the first shot just keep slinging the lead and use the breath holding mechanic to make them run in slow-mo.
If you want to try a slower method but will earn you more gear points then use the bear den area of the Northeast map. Set the time to 10:00 and at the bear feeding area in the valley just south and west of the starting spot there will be a bear. If not restart the hunt. Just make sure you hit the vitals with the first shot and you will get gear points. You can get over 5000 after you complete the pro slam and unlock the pro multiplier