"I want a bag in a different color."
There are two points to explain. Once, some words which have kanji are written in kana : it's often because kanji are so difficult to write that people tend to use mainly kana for an easier reading and writing (if it's handwritten). It's the case for カバンand メガネ Then, you maybe learnt that all the foreign words are in katakana, but sometimes for the impact on an advertisement, presentation or something else, Japanese would use katakana instead of hiragana, since the former has more "sharpness" while the other seems "smoother" and blend more in the ground. By the way kanji looks more "fancy".
So the answer is : it's a matter of habit, and place where the word is used. I hope it helped. :)
Yeah, I suppose that makes sense theoretically for the bag to own the color, but think about it literally; 違う鞄の色 would translate as "a different bag's color." While that is correct grammar in both languages, it's not the right thing to say in this context. "I want a different bag's color."
「鞄の色」color of the bag
「緑色の鞄」bag of color green
since you want the bag, not the color, you say「鞄が欲しい」and the rest is an attribute of 鞄 as「違う色の鞄」"A bag of a different color".
However, you could say「鞄の色」if you are comparing the colors or talking about the color of a bag in specific「鞄の色を確認する」"I will check the color of the bag", in that case you are using the color as an object and the bag is the attribute of the color.
「違う鞄の色が欲しい」means "I want a different bag color" and while that's perfectly fine in English, in japanese you sound like you are making bags and you want to add a different color to the palette of the bags you make. And I think in that case you would just say「違う色が欲しい」which is also perfectly fine in this context about picking a bag, you don't need to specify to the clerk you want a different bag, you just want a different color.