A folded up bike in a duffle bag is NOT FUN to carry around. Figure 24-26 pounds for the bike and bag. Best case scenario, you ride and wheel the bike all the way to the train platform, then bag it up and haul it inside the train car, leaving it in a luggage rack near the door. That might be OK. But if you have to fit it in an overhead luggage rack, for example, that's going to suck.
Reasonable choices in this scenario are the Strida and CarryMe (which are so unlike regular bikes when folded that you might just be able to get by without a bag). I haven't ridden either but I think the Strida is reasonable for a 12-15 mile ride. I don't know about the CarryMe.
You might also look at the Brompton...er., you said inexpensive, scratch that. The Downtube Mini may be an option (although it is heavier and larger than the above two options).