Bring（something or someone) somewhere has the same meaning as “take”. In this case, “I need to bring my car into the shop”—means that you need to take it to the shop. This sounds like you are talking to someone at the shop because you are talking about giving them something that you will “bring/take” to them. If you were talking to someone who was with you, it would be more natural to say, “I need to take my car to the shop.” I hope this helps!