My daughter gets this a lot. I've read that some people have thinner sinus/nasal walls than others, and are more prone to nosebleeds, especially when the air is dry or it's allergy season.
I use saline nasal spray for my daughter, and keep a humidifier running in her room during the night while she's sleeping, and even throughout the day when the air is particularly dry.
I haven't really had to put anything into/onto her nose aside from the saline spray, but I would use lanolin rather than Vaseline if you feel that you need to do this. Petroleum-based products such as Vaseline or lotions/creams that contain petrolatum may irritate baby's skin, and may even be carcinogenic. I've also heard that coating the inside of the nose or the nasal passages with Vaseline or things like Vicks or Mentholatum can lead to lung problems, as the product breaks down and is breathed into the lungs. Lanolin is used for breastfeeding moms, so it is safe for babies to ingest.
Good luck.