I have two children that get spontaneous nosebleeds. My ped said not to worry unless the bleeding continues for more than 60 minutes. It is true that the loss of blood from a nosebleed is not as concerning as other types of injuries that bleed, but it is a concern and a pain to deal with when you don't know when it will occur or for how long.
The two options are typically live with it or have the vein caurtorized (sp?). The latter is when a doctor burns/sears the vein to keep it from bleeding. I come from a "nosebleeding" family and several of my brothers had to have this procedure done. It is not 100% foolproof, and it is rarely recommended and only for severe and extremely frequent nose bleeding cases.
The typical option ("deal with it") is something that you will have to work out for your situation, and hopefully, these responses will give you some ideas to try.
My children are more susceptible to nosebleeds during allergy season (spring) and the cold, dry winter months. During these months, I use a cotton swab to gently coat the insides of their nostrils with Vaseline in the morning and at night before they go to bed. In the winter months, I run a cold mist vaporize to add humidity to their rooms. They like to bundle under their covers year round, but I have found that if they get themselves too hot, it spawns a nosebleed. I let them fall asleep as they like, then remove some of the coverings later so they won't overheat.
I have also made sure I kept a cloth in a baggie on hand at preschool and in my purse just in case. I found a character cloth that my child picked out that was their special cloth for those "silly nosebleeds" (this also helped to keep them calm about the whole thing). Now they are in elementary school and the school nurse has one as well. Fortunately, between the extra care and them getting older, the nosebleeds have lessened.
Continue to reassure your child. Try to make it seem more like an inconvenience than a concern so he will have that same perspective and not be upset by the nosebleed episodes.
Also, to treat the nosebleeds, make sure he is upright with his head in a normal forward position (do not have him put his head back)- you want the blood to flow in order to clot. Be sure to put pressure (whether with your finger or better yet, with a cold, damp cloth) on the end of the nose cartlidge rather than simply closing the nostril. If you can, get your child to do this, so he feels in control and will learn what to do if a nosebleed happens when you're not around. If the bleeding seems persistent, put something cold (I usually use another damp cloth) on the back of his neck. This helps slow the blood flow which comes from the back of the neck, up and over the top of the head. You may need to rewet the cloth with cold water for prolonged bleeding.
Try to read to him to keep him calm and still for at least 10 minutes while you try to stop the bleeding. If the bleeding does not stop, continue pressure until it does (we've sometimes had to do this for 30 minutes).
After it does stop, be sure your child isn't too rambunctious (engaging in overly active play) right after or the bleeding may start up again. We usually sit and color or do puzzles as a way to give the nose and my kids extra time to recover.
I would bring it up with your ped. They need to have this history, especially if the nosebleeds become a serious matter and require more extensive treatment despite how unlikely that may be. They may also have some other suggestions on what to do to help you handle these epsiodes.
Hope this helps.