I created a new character, and the first thing I did was grab my horse, and head to the vampire shrine. Received a bite in 5 seconds (thank you kind strangers on PS4) and managed to become a vampire in maybe twenty minutes,at lv 5 (I didnt check the time but I had to wait a lot for the mobs to respawn). I used the same method that everybody uses at low levels:
https://youtu.be/oqHNOkY_U94
It was easier than I expected, and now I am almost dancing around of happiness xD I have another vampire but with her I got bit at around lv 17 if I am not mistaken so that was very easy.
Here is my pretty vampire lady:
Before

After

I used a lv 3 heavy armor from Varen, (I think) some light pants, and a lv 3 bow, so it is definitely possible to become a vampire at a very low lv. However it still doesnt make much sense since at a low lv your vampire skills level up VERY SLOWLY, but if that is not important to you and you just want to bite people around (like me) then definitely give it a try
I like sweetrolls and I cannot lie