my first teacher and current music mentor, is an accomplished keyboard player, but he started out many years ago playing guitar. he taught me the fundamentals of the bass, and because he's well versed in his music theory he taught me concepts and how to approach playing. His playing style on bass is funk, with some blues.
BIG TIP #1: Get someone who can tell you why they're playing whatever particular things they're playing in addition to showing you how.
when he said i was ready to go to the next level, but he couldnt take me there, he introduced me to a bass player that he worked with many times. so i started taking lessons from him. He was able to help me with my technique, as well as learning to hear and play in the context of a bass player. His background was r&b and funk. He helped me advance, but i was missing application of some things because all he did was play bass.
BIG TIP #2: Someone who plays something other than bass is a PLUS, especially KEYS. That way they can play some things for you to fill in on the bass, so you can learn HOW to use the things that you are taught as well as get practice playing with others as well as keeping your timing on course.