Mandalay is not that far from Bagan. I believe it is about 170 kilometers by road, and if you need to make that trip to catch your flight, there are a lot of very comfortable and reasonably-priced buses waiting to take you. Some of them will even come to your hotel and pick you up there and drop you off at your hotel in Mandalay.

You can also get to Mandalay by train. That would likely take a bit more effort on your part to figure out when the trains go and how you buy tickets and sorting out the different classes of ticket (if any). It would take a fair bit longer than a bus, too, but it would be much cheaper and certainly a lot more interesting as an experience.

Finally, you can go by boat – a tourist boat, to be exact. There appear to be at least two companies operating boats that regularly make the run between Bagan and Mandalay. They don’t run year-round, though. During some months of the low season, they stop operating, and they start back up again once the tourists return.

I appeared to have arrived in Bagan right at the beginning of the new season for the boats. It took some work on my part and a few visits to some ticket offices to sort it all out, but I eventually figured out which boats were going and on which days. I made my final decision to go by boat and bought a ticket. After all, I had taken a train to get to Bagan. And I don’t like buses in general. So a trip by boat seemed the best choice.