What's better than turning into a bear? Turning into a raging bear of course!Hold the phone, this sounds very intriguing.
1 level of barbarian and 3 levels of druids bring the build "online", but is at its best at barbarian 3 (bear totem) and druid 6 (circle of moon).
At level 3, moon druid allows you to transform into a brown bear (CR1). Circle of Moon allows you to transform as a Bonus Action, but the wording of Combat Wild Shape doesn't seem to prevent you from doing so as an Action like regular wild shape feature. This allows you to wild shape and rage on round 1, thus capitalizing on damage resistance on your bear (or wait for rage if you don't think you'll be attacked until your next turn).
You can heal as a bonus action each round as long as you have spell slots, which is arguably twice as useful because of rage, which you will need since your AC will be poor (unless your DM rule that expending a spell slot = casting a spell, but again I think the wording of Combat Wild Shape specifically goes around "casting a spell")
A rush to Druid 6th level gets you a better bear (cave bear CR2) and hits count as magical, which you probably need by then. After that, two more barbarian levels give you resistance to (virtually) all damage via bear totem, reckless attack, and advantage on dex saves. From then on you can do whatever you want.
You are not dependent on ASI or even the extra attack feature. As a matter of fact you get your "second attack" at level 4 in bear shape. And when that doesn't work, you are still a druid...
Alternatively, once you got to barbarian 1 / druid 3, gain two more barbarian levels right away to go berserker for an extra bite attack, but your extra attack as a bonus action competes with your bonus action healing.
The biggest drawback is that your bear form quickly falls behind at higher levels, and none of the dinosaurs refluff well as a bear. At druid 10 you can become an elemental bear for a more spirit-type transformation, but only once per long rest. Or multiclass again into fighter for a more proficient bear? IDK...