Nose bleeds in an older dog are a serious problem. If the antibiotics and vitamin K did not help, the next step is xrays. The biggest concern is a tumor in the nose, as your vet suspects. Other possibilities include foreign bodies (like blades of grass), or bacterial or fungal infections.

I don't know why your vet has recommended a specialist for some preliminary xrays. Most vets will do these. Perhaps you could discuss this with your vet or go elsewhere for the xrays, other than a specialist (to save $$). Your dog will need some sedation, and then the xray can be taken. They can also flush the nasal cavity and look for foreign material, and it is possible sometimes to collect some of the material flushed and look under the microscope to see if there are any abnormal cells. This procedure should not cost an excessive amount of money, and in our clinic, it would run about $150. We would require blood work first to check organ function and blood clotting tests, if that hadn't been done already, and that could add around $100-150. (Every vet clinic is different, and prices vary around the country, but this might give you an idea of cost to start; always ask for an estimate first)

Depending on what is found, other tests that could be run are rhinoscopy (taking a camera into the nose to see if there are any visible abnormalities), and either a CAT scan or MRI. These tests do cost a lot more, and don't fit into everyone's budget.

If there is a suspected tumor, depending on how severe it is, surgery can be done. However, you are talking about a major operation that will cost a lot of money, as it HAS to be done by a specialist. Plus, it may not prolong life very much and is very painful, with a potential for a difficult recovery. Then radiation may have to be done if all of the tumor could not be removed.

I always recommend xrays and nasal flushing to get an idea of what might be going on. I don't always push treatment when there is a suspected tumor. But, I do want to know that the bleeding is not caused by something curable, like a fungal infection, bleeding disorder, or a foreign object. So, I would urge you to consider the xrays and blood work at least, so that you can make an educated decision about what to do.

Please reply if you have further questions.