There's really no inherent difference in meaning, so there's no compelling reason to use the second structure. You could change the nuance of either one in speech by placing the stress on different words. If you stressed "green", you could let your listener know that you have a bag that's not another color like blue or red. If you stressed "bag", you could let your listener know that's you have something that's green but it's a bag and not a ball or a box or anything else. If you stressed "have" you could your listener know that you have one now. If you stressed "a", you could make it clear that you only have one.

The purpose is to call special attention to the greenness of one of your bags.

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您好！后一句从句，修饰bag这个名词，使句子修饰词部分的功能显得更严谨些。