Hello Gulliver. Difficult one this is. A mass usually means a cyst or a tumour. I think your vet should have been more specific, as a mass in the kidney could be either hopefully benign, or malignant. He obviously didn't suggest a biopsy to discover which, or perhaps he considers the mass to be so large that it is causing the problem of blood in the urine.
If that is the case then it is likely that removal of that kidney would be the best option. As to the vet saying you could take a chance on the kidney that has stones, he really should have told you how many (large or small ones), and he could have shown you the picture of the scan. In humans kidney stones can someimes be passed out of the body naturally, although the passing can be painful, so the vet might think that it is the best option to take a chance. Especially as the dog is not old. I think your best thing to do is to speak to the vet again, and ask for a much clearer explanation, before it comes to having to make a decision. At least now you have some questions you can ask. I'm so sorry your dog is having to go through this, and I wish you all the best. Please let me know how you go on. Regards. Schutz.