Unfortunately, because Myanmar is halfway around the world, the flights there will be very long, with at least one stop. The best travel time you're going to get is about 20 hours with one stop, and that's an expensive air china flight. Once you are in Myanmar you will travel between the three cities you are primarily visiting with short plane rides, with an occasional car drive.
JFK to Mandalay
Mandalay to Bagan
Bagan to Yangon
Yangon to JFK
I was unable to find a consistent price for a taxi, but it is clear that it should take about 90 minutes and will cost about 5,000 kyats (A few bucks).
I found lots of car rental agencies in Yangon, although I am unable to access their websites due to them being blocked. But I can see that on google maps there are many car rental agencies, so you should have no trouble finding a car. The drive should take about 40 minutes.
Estimated travel costs: Around $2,000 for one person
2x= about $4,000 for two people