Hi,
The most common causes of random 
nosebleeds are as follows:
- Since there is bleeding from one 
nostril only, some malformation of blood vessels in the same side can be the cause
- Bleeding from Little's are from 
nasal septum due to no support to the blood vessels
- Infection and inflammation due to 
sinusitis and rhinitis
- Some mass or tumor
- 
Hypertension not detected till now
This can be diagnosed by the following ways:
- Consult an ENT Surgeon for nasal endoscopy
- CT scan of nose and sinuses
- Arteriography if indicated
All these will give the proper diagnosis and thus allow a specific treatment as per the cause found.
Take care. Hope I have answered your question. Let me know if I can assist you further.
Regards,
Dr. T. Chandrakant, General Surgeon