Welcome to the place to learn the German Language! Come here to discuss topics or quirks related to the German language, ask any questions about learning German, provide tips to current learners, and share your journey through the German-learning process!
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Not a native speaker, but I think "ich komme mit dir zur Bank mit" would be grammatically correct, but normally you would just say
Or maybe
But I don't think you need to say "zur Bank" or "mit dir" since that was already mentioned. Hopefully there's a native speaker who can correct me or add to that if needed.
Native speaker here and I couldn't have said it better.
Both of your examples are correct and natural and OP's sentence is indeed gramatically correct and also pretty natural but would get abbreviated, in practice, the way you described.