Translation:The black bear is eating an apple.
In the nominative case, the adjective modifying a masculine noun does not take an -r ending when used in conjunction with the definitive article (der).
I'm not sure how to associate the right color form to the noun. In other words, how would I know to use "schwarze" (black) with "Bär" as opposed to or "schwarzen"?
And I can just assume that "Schwartz" is the color as in noun and not to describe the actual black color of an object?
"Das Schwarz" = the color black
"schwarz" = "black"
The ending of an adjective (like "schwarz") depends on the following noun (its gender and case) and the article before. "Bär" is in nominative here and a masculine noun, also you have a definite article before the noun, hence the ending is "-e". You would for example use the ending "-en" if the bear were the direct object of the sentence. "Ich sehe den schwarzen Bären." = "I see the black bear." Look for example here for all three tables: https://en.wikipedia.org/wiki/German_declension#Attributive_adjectives
I hope I could be of help.
is the direct object of this sentence then the apple? as it is the thing having something done to it?
In English when we say 'black bear' we mean a specific type of bear, as opposed to 'brown bears', 'Grizzly bears', 'polar bears', etc. Is the same true in German, or would this only refer to the bear's literal colour?
Seems to be Schwarzbär
https://de.wikipedia.org/wiki/Kragenbär (aka Asiatische Schwarzbär)