IF I had to use my small fixed blade knife similar in size to your Seal Pup, I'd use the grip that many knife fighters/martial artist favor.

With you thumb on top, you grip knife so blade is pointing down/with edge facing target.
You can slash up/across and stab on the down stroke/backstroke.
Another thing I read about is how to use your "off hand/arm" ?
If say you keep your left arm horizontal, the bear will bite your wrist/forearm. I don't know if you could stand the pain from that and even if you could, he has the leverage on you, plus he's swinging those two big paws.

In the military I was taught that if attacked by a sentry dog, you had to accept being bit but you could use that against the dog which is trained to grab ahold and hang on until called off.

The idea was to offer your forearm ( easier said than done) before the dog can go for the jugular.
You jam your forearm into its jaws to the point it can't get close them and push back into the dog, raising it onto it's back legs.

Then you have two options. If you have a knife, you gut it with your free hand.
The next option is harder but doable.
While the dog has your left arm, you grab its fur at the neck and drive your knee upward into chest area, hopefully breaking ribs and puncturing a lung, either killing it or making it let go.

I doubt you could do that with a bear, much to strong and well muscled.
What you want to do ( again, easier said than done) is keep your off hand perpendicular to the bear and try and secure hold on the bears throat area while stabbing and slashing with knife hand.
Go for eyes/into ears, hopefully into brain which would kill instantly.

If you find yourself going to ground, you don't want the black bear to be on your back, going for a fatal neck bite.
You want to be on your back, with ankles crossed and knees pulled into chest.
The bear will go for entails first. Hopefully this will give you the time to deliver a fatal blow. :-/

OR if your in the US and you can carry a weapon legally, you hit it with the bear spray and if that doesn't work, you pull your pistol and blows it's brains out. ;)

If that offends your wilderness ethics, then go for the first option and hope that works.