If you are on PC you can simply ask around in guilds and a lot of people are willing to give you the bite for free.
I am not sure how it is on consoles, might be difficult having no chat.
Based on all the requests we've seen posted by folks looking for vampire/werewolf bites, we've created individual threads for players on each console server to coordinate these bites. Our hope is that this will make it easier for those interested in acquiring and/or spreading vampirism and lycanthropy to do just that. Please use the thread for your console and server to post what you're looking for or find willing victims.
Additionally, we don’t allow trading or selling on the forums, so if you’re looking for a bite, or what to offer, it needs to be a free exchange. Thanks!