Here’s a quick and easy guide for how to get all the new bear forms that have been introduced in patch 10.2 for Dragonflight. The new forms are definitely worth getting, a couple of them required to kill some rare Elites but you can easily solo them. 

How to Get Druid Bear Forms in 10.2 WoW Dragonflight - Best Ways to Unlock Druid Bear Forms 

1. Runebear Form & How to Unlock

It has a chance to drop from the new world boss in the Emerald Dream, we are not sure at what drop chance is at, but hopefully it's not too low, probably won't be too bad since we'll most like be killing the world boss every week.

- Locate and defeat Aurostor the Hibernating, the World Boss in the Emerald Dream.

- After defeating Aurostor, there is a chance for the Runebear Form to drop as a reward.

2. Brown Umbraclaw & How to Unlock

For the umbraclaw forms, there's 3 different ones, we'll start off with the brown one. You need to buy a silent Mark of the Umbraclaw from Thaelishar, Groveheart at coordinate 60.17. You then need to use this item on 10 of the Umbraclaw throughout the zone to learn the form. The item will then transform to the item you need to grant the form. The best places to do this is on the Southwest bottom of the map at coordinates 38.72. There's usually around 7 or 8 right there. When you use this item though, it does put a 5 minute debuff on them, so you can't use it again on the same one right away. So you can either wait choose to wait 5 minutes to use it on the same ones or you could kill them to have them respawn.

3. White Umbraclaw & How to Unlock

To get the white umraclaw form, you need to do the emerald bounties. These are three minute events that are always active around the emerald dream. They look like seeds and it's where you'll plant a seed and then nourish it. It'll give you a chance to drop from those. You can nourish these by giving them do drops that you'll obtain throughout the dream by doing quests events or even helping the sething to grow in that area that can mean picking some weeds, stomping on bugs, killing lashers to help nourish it and it'll give you more do drops. These Emerald bounties are farmable, there are 3 different levels of them, the small dream seeds which are uncommon, those are the green ones. The plump dream seeds which are rare, those are blue. And gigantic dream seeds which are epic and can only be planted once a week per character. The better the seed ,the higher chance of better rewards and the form. You can get these different seeds throughout the emerald dream but specifically from doing the weekly Super Bloom event. It has a pretty high chance to drop especially with doing plump dream seeds or above. 

4. Black Umbraclaw & How to Unlock

To get the last umbraclaw form, you just need to kill the rare mosa umbremame at the coordinates 54.37, she'll spawn right at the back of this cave and it has a chance to drop from you. 

5. Ash Bristlebruin & How to Unlock

This one is incredibly easy to get, all you have to do is grab the item pollen fuse bristlebruin fur sample at coordinate 63.39. Once you grab this, you can use it and then you'll have the form.

6. Green Bristlebruin & How to Unlock

To get the other bristlebruin form, the green one which is the last bear form we have, it drops from the rare morag, the slothful in the back of the cave. Coordinates are 39.71. It's not a 100% drop chance, but it may be pretty high.