If my wife and I return to Romania in 2023, we would like to travel from Cluj-Napoca to Bistrita. What is the best way to travel there and back? Rental car? Train? Other public transportation? Hired bi-lingual driver?

Take the train
have a look at rome2rio and seat61.com

Train doesn't look super fast but by the time you messed around with a car, you could probably be there by train. Looks like about 2hrs 45mins with no changes. Romania rail site isn't loading for me at the moment but interrail.eu shows the routes.

Now that I've started the research for a trip to Transylvania in the fall, I would like to make a contact with someone at one of the Cluj-Napoca universities that I could talk to regarding history of the Saxons who lived in Transylvania for centuries. I want to be better prepared for our next visit. Any advice and contacts provided will be appreciated.