Buses only run until 10pm, so at that point, you're down to walking, hitchhiking, or taxi.
Note that most taxis tend to be older, often diesel, often Mercedes. After 10pm, there's often a 30% surcharge. Tipping isn't expected, but the driver may not choose to use the meter unless you specify, so make sure you either have him using the meter, or negotiate the price beforehand. From the airport to town should be around 100,000 Gs ($US25) to the centre. It is possible to get a cheaper fare by walking up to the main road and taking a yellow cab from there.
Is it safe? That's, sadly, a subjective question. There's always a danger of problems, anywhere in the world, just less/more in some places. However, consider that it's at night, with fewer 'witnesses'. So pick a company with a name, try to choose a taxi driver who is chatting with other drivers (ie they know him and he's not a stranger). Make sure the hostel knows you're coming - perhaps ring and tell them your license place before departing, if you can. Take note of the taxi driver's details if he has them visible, and if his name is there, say something like 'thanks Pedro' or whatever when you get in, so he knows you've seen it and can identify him.
Put your gear in the back seat, NOT the trunk/boot, so that if he's trying to be difficult or ask for more money or something, you aren't relying on him opening the trunk to get your stuff - you can still make a getaway. I've had to do this in the past and it's not fun.
There's also an airport information desk that you could use to book a taxi - they'll know who the good companies are.
Finally if you want to book one before you go, you could book a private car beforehand, which seems to be reasonably priced...but may not speak English (need to inquire).