I personally have never used a .444 on black bear, but believe that it should be an excellent choice for blackies within the effective range of the cartridge. The Hornady "light mag" round should fill the bill nicely.
The only word of caution when using the .444 Marlin on heavy game such as bears or big hogs, is to make sure you are using the right bullet. Some manufacturers load the .444 with lightly constructed bullets (240 gr. H.P.) that are designed to perform at .44 magnum pistol velocities. When these bullets are driven at the higher velocities of the .444, particularly when shooting at muscular / heavy boned game, they tend to "blow up" without providing sufficient penetration. This leaves you in the precarious position of having to track a wounded, ****ed-off, toothy critter which is one scenario we all try to avoid.
Hopes this helps you in making your decision. Good luck & good hunting!