Some say they compliment each other well... Others say you should not use them together. Lots of people have them running side by side with no issues at all.
There is a mountain of research you can do on it, but I think it comes down to your individual set up. If it works for you, I'd say use them both. I've had Malwarebytes PRO since around 2007 and aside from one issue, it's always been a great tool.
malwarebytes is designed to not conflict with others. in rare cases where it occurs, you can white list it in the main av preferences (and malwarebytes pref's). bitdefender is one of the best performers in all labs: it doesn't need much help. but yes, malwarebytes will make your system more secure (particularly with zero day threats). it depends on you and what you do on your system ... as to whether you need it or not. it will add weight, cost, and security.
download the free version. it will give you a trial of the full for free. then you can evaluate it yourself. its a nice program by an excellent company. i recommend it. it demolished iobit's malware fighter in these tests: