getting from FCO to Travestere

According to the timetables at www.bahn.de, there are regional trains that go directly from Fiumicino to Ostiense and the trip takes 30 minutes. To see for yourself, go to the site and click on the drop-down menu in the upper right-hand corner for English. Enter Aeroporto Fiumicino as your departure point and Roma Ostiense as your arrival point.

I have no idea what the bus schedule will be on 1 January. I imagine you could take a taxi from Ostiense to the hostel. According to viamichelin.com, it's 3km from the piazzale to the bridge.

I would agree that a taxi from Ostiense might be the easiest, make sure you go to a taxi stand/line, rather than just a taxi on the street. Maybe go further and ask your hostel what the fare should be, and ask before you commit. From FCO, the train you want is a regional train, with the destination as mentioned (Orte or Fara Sabina) I think the cost is like 5.50 euro. Do not take the express to Termini, and other than that, there may only be one other route that leaves from FCO, so it is pretty easy. Aside from that, the bus is relatively easy, the only hitch I noticed is that some buses have better signs in the bus to indicate the stop, in other cases it is not clear, and the bus stop may not be well marked.

The stop just before Ostiense is Trestevere. It sounds like you might be just between the two. For reference, Ostiense stop is at the Piramide Metro Stop - they are actually side by side. I agree with the others, that you would be better off with a taxi whether you use the Ostiense or Trestevere stop. Busses are wonderful when you don't have luggage AND you know where you are. Besides, the Ostiense/Piramide stop has about 5 different places to catch the bus, so you might spend more time looking for where the bus is located.