There are several of them, some of them are private while most of them depend from any of the two main Universities in Bratislava.
Right now I just have info about the Comenius University dormitories, the rest will be added soon.
For Comenius University there are two main options:
This amazing Gulag-looking building complex (main picture) will feel like your second home, don't be afraid by it's scary exterior (even if it was repainted not so many years ago), is actually much better than expected.
There are several room options, but most common is the 6 ppl room, which divides in a common area with a small kitchen, fridge, 6 wardrobes, a toilet and a bathroom, and in two sleeping rooms with 3 beds each, so in the end you just need to “live” with 2 more other persons. The sleeping room is bigger than the average dorm room and it has three desk, enough space for all your clothes and stuff (really, it has a lot of shelves and small closets, the space under the bed is also avaliable) so there is not a claustrophobic feeling at all. The room itself is 90's at it's best, but come on, we are students and we can live with that. You can decorate it as you like since there is not furniture restriction (but is wise to agree with your roomates). The main disadvantage of the room is that there is not microwave, and you are not allowed to put one inside, as well as an extra fridge, but you may end up eating in the canteen so it is not really a problem. There are also rooms for 4 and 5 people, with a combination of two 2-bed room or a 3-2.
About the facilities, It has two canteens where you can eat for just 2,2€ with the student ticket (bought inside from 10 to 13:30 everyday), the canteen is open at early morning the morning but they accept tickets just from 13:30 to 21:30.
There are several doctors in the building, so if you have a non very serious emergency you can go to them, most of them know English. There is a technician as well, in case you have some problem with your computer. In the D1 block there is a small shop for food and a printing business where you can print for 3 cents a page. There are several study rooms so you can study there in the case of a noisy room.
It also has a bar (Havana bar) in the building and also you have the oportunity to have a massage in RelaxDruzba. The internet is wired (not wifi) but is incredibly fast, with downloading speed up to 10mb/s. You can change your sheets from bed once every 2 weeks and also there are washing machines in the 5th floor as well as drier for particular use (about 2-3€ per full cleaning and drying).
If you want to party but don't want to walk far you are lucky, there is a nice disco just 50 metres from the dorm, Kings Rock Pub, which makes a huge party every tuesday.
But the best of this dorm is how easy you can go to centre, you have more than 7 buses or trams in that direction, so you will not wait more than 2 minutes if you want to go to Old Town. Trams 4,5,6,9 stop just in front of it, and there are bus stops at both side of the road which can take you to more far away places like train station (bus 32) or Eurovea (28) or Devin castle (28 westbound).
If you want to buy cheap food you are lucky, just 300m or 1 tram stop westbound there is a Lidl supermarket, where you can find the best prices in the city.
Everybody needs a dorm card to go inside, you receive one for free once you register, but if you loose it you need to pay 16 €, same happens with the keys but in this case you need to pay a fine of 115€. The dorm takes an extra 160€ during your stay working as deposit, which is returned if not troubles were caused. For non residents in Druzba, they can spend the night for 4,1€ but it doesn't mean that they have a bed to sleep in, so you will need to accommodate them somehow (In my case I have a sleeping bag when visit comes).
There is a botanic garden (Botanicka Zahrada) open during spring and summertime closeby, as well as a veterinary clinic (you will hate the two guardian dogs in the night). There is also a gas station open 24/7, so if you need something in the night, you can get it there.
In order to book a spot, you need to contact them throught this link and pay the requested ammount by bank transfer.
Since I don't live here, I will let this part for a person who resides there, avaliable soon
This is the definitive guide for a Erasmus or a Student in Bratislava, all info I know about the city will appear here