My wife and I are planning a trip to Mosel this spring and are looking for advice on how to best get around. We likely will be staying in either Zeltingen or Bernkastel and debating whether to rent a car or not. I’ve heard most car rentals in Germany are manual transmission, which I’m not used to driving, but does that mean there are no rentals with automated transmission? If we don’t rent a car, how easily available are cabs, buses, or Uber/Lyft in the region?
You need a car. Or a full time driver but a car is more practical.
For sure you can order an automatic from a major airport.
We spent one day in Frankfort and rented an automatic from Hertz at the Hertz near the train station.It’s about a 2 hour drive to the Mosel.We stayed at the sa prum guest house in Wehlen witch is
half way between Berncastle and Zeltenger.It wasn’t elegant but served well.Zeltengerhof was an ok restaurant near there.Good to have a car to drive to the wineries.
Yes, it’s pretty hard to move around there without a car (or driver). And if you want an automatic, arrange in advance (or at least be sure they are available), IIRC that’s not standard at all (no pun!)
A car is a must. There are automatics to be had, just book in advance.
Has anyone ever flown into Luxembourg to get to the Mosel? It looks to be only an hour away. Any issues finding automatic cars to rent there? Never driven in Europe before, any issues with border crossing? 
If we flew into Luxembourg, is there anything worth checking out there for a day or two?
This. “American” companies might be better bet than Sixt or Europcar
I’ve flown into Lux and stayed in Trier about 40 times. I’ve never ‘needed’ an automatic but I have been given one plenty of times. Just check online.
Luxembourg itself is quite pretty. Worth a day I’d say. The Sofitel Grand Ducal is nice and a couple of hours exploring the Grund.