A PC in our group was off on his own following a recurring villain of our groups. He was paralyzed where he could move, and the vampire bit his neck. The vampire said "now you get to remain 19 (years old) forever" before he left the cave. This was all done in RP.
We found him later, and healed up his bite marks. Our characters know of vampires, specifically only the one that bit him (recurring villain), but don't really know how vampirism works, because it isn't a super common thing in this world yet.
My question as the player is:
How does RAW vampirism work in 5e?
Is it a disease that develops over time? Is it something where they have to die and be brought back as a vampire?