You're very welcome for the informative posts .
The Bus station is in Nyaung U, just next to the Shwezigon pagoda, so to go to New Bagan there should be around eight to ten kilometers, it would take you about 10 to 15 minutes by car I think and then, horse cart maybe something around 30 minutes. Not sure about the price though, I know that for one day it is around 25000 kyats, to go around Bagan by horse cart. Then for one trip, considering they will charge you proportionally more, you may be asked 4000 or 5000 kyats I think. But if you are not in a hurry you can take your time to negotiate!!
You have some guest houses in New Bagan, but never stayed there. If you know when you are traveling, it may be safer for you to find your guest house in advance and book it. Bagan is getting crowdier, and even if you go during hot season (starting around now and until June) you may face shortage of rooms.
Have a great trip,